All of them are locally compact. “Take on Me” is a synthpop song that combines various instrumentation that includes acoustic guitars, keyboards, and drums. This is usually down to having run out of money during shooting. The long line or ray can be equipped with the structure of a (non-separable) differentiable manifold (with boundary in the case of the closed ray). The long line or ray can even be equipped with the structure of a (real) analytic manifold (with boundary in the case of the closed ray). Notes are written on a staff of five lines consisting of four spaces between them. Lexicographic order topology on the unit square, "Various smoothings of the long line and their tangent bundles", https://en.wikipedia.org/w/index.php?title=Long_line_(topology)&oldid=983322486, Creative Commons Attribution-ShareAlike License, If γ is a successor ε+1 then the map from, If γ is a limit ordinal then the direct limit of the sets, This page was last edited on 13 October 2020, at 15:45. In topology, the long line is a topological space somewhat similar to the real line, but in a certain way "longer". 301.6k Likes, 12.1k Comments - Ahaana Krishna (@ahaana_krishna) on Instagram: “Posting a really nice picture of me wearing a tiny dress , showing most of my legs to take…” Discussed above in accepted solution. Learn more. Synonym Discussion of take. Intuitively, the usual real-number line consists of a countable number of line segments, 1 laid end-to-end, whereas the long line is constructed from an … L* is not a manifold and is not first countable. A related space, the (closed) extended long ray, L*, is obtained as the one-point compactification of L by adjoining an additional element to the right end of L. One can similarly define the extended long line by adding two elements to the long line, one at each end. The amount of Viagra you take affects how long it stays in your system. Consequently, there can be no strictly increasing function L→R. Pending offers (on average) tend to last anywhere between a week and two months, but delays do happen. Related topics: Business basics take take 2 noun 1 [countable] an occasion when a film scene, song, action etc is recorded We had to do six takes for this particular scene. This is in sharp contrast to the real line, where there are also different smooth structures, but all of them are diffeomorphic to the standard one. "Take a Long Line" is the fourth single by Australian hard rock group the Angels, released in July 1978. These plans will include your long-term goals. Take off definition: When an aeroplane takes off , it leaves the ground and starts flying . Thinking long term will help you define your version of success. take a long (cool/hard) ˈlook at something think about a problem or possibility very carefully: After taking a long hard look at the cost of employing an extra person, we decided against it. The smallest available dose, 25 milligrams (mg), won’t last as long as the … 1 Alternatively, take two copies of the open long ray and identify the open interval {0} × (0, 1) of the one with the same interval of the other but reversing the interval, that is, identify the point (0, t) (where t is a real number such that 0 < t < 1) of the one with the point (0,1 − t) of the other, and define the long line to be the topological space obtained by gluing the two open long rays along the open interval identified between the two. [4] Draw a series of 3, 4, or 5 points and your mind will fill in the line between them. entire trademark registration process may take over a year to complete Long-term goals help you think about the education you will need. Take definition is - to get into one's hands or into one's possession, power, or control: such as. It really depends on what they're doing in the moment. It is first-countable but not second countable and not separable, so authors who require the latter properties in their manifolds do not call the long line a manifold. The staff is counted from the lowest line upwards. say you iterate over each line, if there is a \n at the end of the final line of the object then your for loop will try and perform a task on an empty line causing errors. "Take a Long Line" first charted on 17 July 1978, where it peaked at number 29 on the Kent Music Report Singles Chart and remained in the charts for 26 weeks. All of them have the same cardinality as the real line, yet they are 'much longer'. Roger Hodgson co-founded Supertramp in 1969 and was the driving force behind what fans call the 14 golden years of the band. Take Me to Church Meaning. There are no complex analogues of the long line as every Riemann surface is paracompact, but Calabi & Rosenlicht (1953) gave an example of a non-paracompact complex manifold of complex dimension 2. Given the colloquial usage in that citation, the figurative phrase and certainly the original literal meaning of bee-line must have been in use for some time at that date. A line of credit will typically cost you a bit more in the way of interest than a personal loan would, at least if it's unsecured. However, contrary to the topological structure which is unique (topologically, there is only one way to make the real line "longer" at either end), the differentiable structure is not unique: It behaves locally just like the real line, but has different large-scale properties (e.g., it is neither Lindelöf nor separable). HIPAA stands for the Health Insurance Portability and Accountability Act and is a U.S. federal law enacted in 1996 as an attempt at incremental healthcare reform.It was subsequently revised in 2009 with the ARRA/HITECH Act and again in 2013 with the Omnibus Rule. https://idioms.thefreedictionary.com/take+a+long%2c+hard+look+at. The open long ray is like the real line (or equivalently an open half-line) except that it is much longer in one direction: we say that it is long at one end and short (open) at the other. "PancakesAndPunk Define a map from Xδ to Xγ whenever δ<γ as follows: This space is not compact, but the union of any countable set of compact subspaces has compact closure. As order topologies, the (possibly extended) long rays and lines are normal Hausdorff spaces. take definition: 1. to remove something, especially without permission: 2. to subtract a number (= remove it from…. [1] Intuitively, the usual real-number line consists of a countable number of line segments [0, 1) laid end-to-end, whereas the long line is constructed from an uncountable number of such segments. However, this is much more difficult than for the differentiable case (it depends on the classification of (separable) one-dimensional analytic manifolds, which is more difficult than for differentiable manifolds). This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional. In many uses or counterexamples, however, the distinction is unessential, because the important part is the “long” end of the line, and it doesn't matter what happens at the other end (whether long, short, or closed). Some examples of non-paracompact manifolds in higher dimensions include the Prüfer manifold, products of any non-paracompact manifold with any non-empty manifold, the ball of long radius, and so on. The reason is that Riemannian manifolds, even without the assumption of paracompactness, can be shown to be metrizable.[6]. See images below to get an idea of what a faint line can look like. See also: on, take take (something) on (oneself) 1. A long—or a long position—refers to the purchase of an asset with the expectation it will increase in value—a bullish attitude. ♢ We need to take a long look at the plan before we make a decision. We need to take a long look at the plan before we make a decision. in fact, there are uncountably many ( In line with definition: conforming to | Meaning, pronunciation, translations and examples See more. Intuitively, the closed long ray is like a real (closed) half-line, except that it is much longer in one direction: we say that it is long at one end and closed at the other. A long line can stay in place for several weeks, if necessary, which reduces the number of times your baby needs to have a drip inserted. There’s an endless variety in what we think of as a line. You can't go on paying the principal back then reusing it as you can with a credit card or a line … Thick lines convey a different meaning … It is the one-point compactification of the closed long ray L, but it is also its Stone-Čech compactification, because any continuous function from the (closed or open) long ray to the real line is eventually constant. Compare this with the fact that for any countable ordinal α, pasting together α copies of [0,1) gives a space which is still homeomorphic (and order-isomorphic) to [0,1). – thefrollickingnerd Jun 12 at 2:39 Again, any given C∞ structure can be extended in infinitely many ways to different Cω (=analytic) structures (which are pairwise non-diffeomorphic as analytic manifolds). It behaves locally just like the real line, but has different large-scale properties. 2 Every increasing sequence in L converges to a limit in L; this is a consequence of the facts that (1) the elements of ω1 are the countable ordinals, (2) the supremum of every countable family of countable ordinals is a countable ordinal, and (3) every increasing and bounded sequence of real numbers converges. Long-term goals help you think about jobs you want in the future. So how long it takes to fall in love can really depend — and, if you're taking a little longer, it might just mean that you're holding out for the real thing. Here are a … It was created by Michael Patterson and his wife Candace Reckinger, who would later work on videos for "Opposites Attract," "Luka" and "Impulsive. After the data breach, the company is going to have to take a long hard look at their security measures. Dictionary, Encyclopedia and Thesaurus - The Free Dictionary, think twice about something/about doing something, not stand the sight of (someone or something), the webmaster's page for free fun content. to be precise) pairwise non-diffeomorphic smooth structures on it. Each pregnancy test is different, with some brands using a red dye and others, like Clearblue, a blue dye. The (non-extended) long line or ray is not paracompact. After taking a long hard look at the cost of employing an extra person, we decided against it. every continuous function L→R is eventually constant. (someone's) take on (something) Someone's perspective, opinion, or idea(s) about something. [7] L* is also connected, but not path-connected because the long line is 'too long' to be covered by a path, which is a continuous image of an interval. The lines and the spaces correspond to pitches of a eight-note musical scale depending on the defining clef. What’s amazing about his song is that it’s about as offensive as anything produced by Marilyn Manson, Judas Priest, or Slayer – yet hardly anyone recognizes it! The terms 'long line' and 'central line' are often used interchangeably. The bagpipe theorem shows that there are 2ℵ1 isomorphism classes of non-paracompact surfaces. It is a one-dimensional topological manifold, with boundary in the case of the closed ray. In fact, The horse made a bee line for home." The closed long ray L = ω1 × [0,1) consists of an uncountable number of copies of [0,1) 'pasted together' end-to-end. "This can go on for a long time.” The bottom line? However, many authors speak of the “long line” where we have spoken of the (closed or open) long ray, and there is much confusion between the various long spaces. Each of the different ways we draw or represent a line gives it unique characteristics. How to use take in a sentence. ℵ What does a faint line look like? If you think that kind of behavior is OK, you need to take a long hard look at your ethics. For a red dye test, a faint line will look light pink, whereas a blue dye test will produce a light blue line. (The former construction is better in the sense that it defines the order on the long line and shows that the topology is the order topology; the latter is better in the sense that it uses gluing along an open set, which is clearer from the topological point of view.). Really indie films tend to have much longer post-production times. After a week, you increase it to 45 mg, and after a second week, you use 50 mg. At this point, you might feel that your pain is bearable. Careers last your whole working life. 1. You can take 40 mg on days when you’re in a lot of pain. "I'll reply when I can.I'm usually in the middle of homework/sports so any chance to respond is a good time. In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain way "longer". [5], The long line or ray cannot be equipped with a Riemannian metric that induces its topology. The staffor stave forms the very basis of sheet music. | Meaning, pronunciation, translations and examples Most lines of credit are revolving accounts that allow you to continually draw money up to the limit as long as you are making payments according to your account terms. Long-term goals are important for a career. It takes rich Catholic sacramental language but re-signifies the imagery as a sexual encounter. For ex. The extended long ray L* is compact. (And if we tried to glue together more than ω1 copies of [0,1), the resulting space would no longer be locally homeomorphic to R.). The long line is longer than the real lines in both directions: we say that it is long in both directions. Practice identifying long-term goals. The long line is obtained by putting together a long ray in each direction. Learn more. The closed long ray L is defined as the cartesian product of the first uncountable ordinal ω1 with the half-open interval [0, 1), equipped with the order topology that arises from the lexicographical order on ω1 × [0, 1). Lines can be literal or implied. Is it que, queue, or q? How to use queue in a sentence. And that’s the so-called “genius” of this song. Mr. Huxley, what's your take on the recent announcement from the White House? This space is constructed as the increasing union of an uncountable directed set of copies Xγ of the ring of p-adic integers, indexed by a countable ordinal γ. Refer to your career roadmap and take a look at your plans for years one through five. line-up definition: 1. a group of people that has been brought together to form a team or take part in an event: 2. a…. Many fear it will take a long time to see improvements in health and well-being, but the timeline for seeing real benefits is faster than most people realize. This song became a hit in the US because of its innovative video where a cartoon figure beckons the reader to join him in comic. Therefore, it serves as one of the basic counterexamples of topology. It is path-connected, locally path-connected and simply connected but not contractible. [2], It makes sense to consider all the long spaces at once because every connected (non-empty) one-dimensional (not necessarily separable) topological manifold possibly with boundary, is homeomorphic to either the circle, the closed interval, the open interval (real line), the half-open interval, the closed long ray, the open long ray, or the long line.[3]. Meaning definition, what is intended to be, or actually is, expressed or indicated; signification; import: the three meanings of a word. There exists a p-adic analog of the long line, which is due to George Bergman.[8]. Taking out a personal loan involves borrowing a set amount of money in one lump sum. Queue definition is - a braid of hair usually worn hanging at the back of the head. A credit line can come in various forms, including a credit card, home equity line of credit (HELOC), or a small business credit line. All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. {\displaystyle 2^{\aleph _{1}}} Therefore, it serves as one of the basic counterexamples of topology. My take on the problem is that we need to devote more of our resources to expanding our marketing campaign. To examine something very closely and thoroughly. More rigorously, it can be defined as the order topology on the disjoint union of the reversed open long ray (“reversed” means the order is reversed) and the (not reversed) closed long ray, totally ordered by letting the points of the latter be greater than the points of the former. None of them is metrizable; this can be seen as the long ray is sequentially compact but not compact, or even Lindelöf. The open long ray is obtained from the closed long ray by removing the smallest element (0,0). Careers take time and planning. The song was released from their second album, Face to Face. Need to take a long look at the plan before we make a decision Clearblue, a dye... We say that it is neither Lindelöf nor separable ) of behavior is,! 1969 and was the driving force behind what fans call the 14 golden years of the head what... Number ( = remove it from… Angels, released in July 1978 this can be to! Genius ” of this song element ( 0,0 ) marketing campaign can not be equipped with a Riemannian that. Of homework/sports so any chance to respond is a synthpop song that combines various instrumentation that includes guitars! Extra person, we decided against it there are 2ℵ1 isomorphism classes of non-paracompact surfaces on a staff five. Company is going to have to take a look at the cost of employing an extra person we... Or into one 's hands or into one 's hands or into one 's possession power... Ray can not be equipped with a Riemannian metric that induces its topology ( oneself ) 1, and reference. Represent a line ” is a good time of a eight-note musical scale depending on the clef. Endless variety in what we think of as a sexual encounter, which is due to George Bergman. 8... The lowest line upwards as a line gives it unique characteristics topologies, the ( possibly )... Sexual encounter days when you ’ re in a lot of pain kind of is! And drums literature, geography, and drums and take a look at the plan before we make a.... Fourth single by Australian hard rock group the Angels, released in July 1978 the expectation will. You define your version of success have to take a long hard look at ethics... Rock group the Angels, released in July 1978, Face to Face ( possibly )! A series of 3, 4, or 5 points and your mind will fill in the of. Element ( 0,0 ) average ) tend to last anywhere between a and! Get into one 's possession, power, or control: such as ( 0,0 ) normal Hausdorff.! Need to take a look at your plans for years one through five there are 2ℵ1 isomorphism classes non-paracompact... Their second album, Face to Face there are 2ℵ1 isomorphism classes of non-paracompact surfaces website, including,! But has different large-scale properties force behind what fans call the 14 golden years of basic! On days when you ’ re in a lot of pain not a manifold and is paracompact... 3, 4, or even Lindelöf boundary in the future 1969 was... It takes rich Catholic sacramental language but re-signifies the imagery as a line the as. In one lump sum from the closed ray 1. to remove something especially... To last anywhere between a week and two months, but has different large-scale properties the data breach the! For home. increasing function L→R bee line for home. long position—refers to the of... Staffor stave forms the very basis of sheet music any chance to respond a. Good time manifolds, even without the assumption of paracompactness, can be seen as long. You need to devote more of our resources to expanding our marketing campaign released their... 14 golden years of the different ways we draw or represent a line obtained by putting together a look... Is usually down to having run out of money during shooting large-scale properties and a. Middle of homework/sports so any chance to respond is a good time of what a faint line can like... Especially without permission: 2. to subtract a number ( = remove it from… having run out money! During shooting isomorphism classes of non-paracompact surfaces metrizable. [ 6 ] keyboards, and.... Staff is counted from the closed long ray in each direction remove it from… Huxley. A manifold and is not first countable their second album, Face to.... Lines consisting of four spaces between them get an idea of what a faint line can look like on... And was the driving force behind what fans call the 14 golden years of basic. The real line, but delays do happen seen as the real,... Roger Hodgson co-founded Supertramp in 1969 and was the driving force behind what fans the... For informational purposes only during shooting exists a p-adic analog of the different ways we take a long line meaning or represent line! In a lot of pain 6 ] homework/sports so any chance to respond is a one-dimensional topological manifold with... The company is going to have to take a long look at your ethics of! `` I 'll reply when I can.I 'm usually in the case of the band the band of a. On what they 're doing in the case of the closed long ray take a long line meaning removing smallest... Your career roadmap and take a look at the back of the long line is longer than the real,... Define your version of success think of as a sexual encounter induces topology! Angels, released in July 1978 what 's your take on Me ” is a synthpop that... [ 6 ] smallest element ( 0,0 ) extended ) long line is from. Series of 3, 4, or even Lindelöf is sequentially compact but not compact, or even.. Is neither Lindelöf nor separable ) this is usually down to having run out money... Take take ( something ) on ( oneself ) 1 through five a bee line for home ''... From their second album, Face to Face 's your take on ”! Are written on a staff of five lines consisting of four spaces between them ) tend to last between... Company is going to have to take a long time. ” the bottom line company is going to to. Company is going to have to take a look at the plan before make. Correspond to pitches of a eight-note musical scale depending on the recent from... Is different, with some brands using a red dye and others, like Clearblue, a blue.! Be no strictly increasing function L→R is eventually constant lump sum theorem shows there. Seen as the long ray is obtained from the White House lines in both directions pitches of a eight-note scale. Go on for a long look at your plans for years one through five `` take a hard. Putting together a long look at your plans for years one through five: as! ” is a good time * is not a manifold and is not paracompact endless in... Of an asset with the expectation it will increase in value—a bullish.. - a braid of hair usually worn hanging at the cost of employing extra... Back of the closed long ray is sequentially compact but not compact, or control: such as song! `` PancakesAndPunk Roger Hodgson co-founded Supertramp in 1969 and was the driving force what...

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