If you think that kind of behavior is OK, you need to take a long hard look at your ethics. As order topologies, the (possibly extended) long rays and lines are normal Hausdorff spaces. These plans will include your long-term goals. 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. 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. Refer to your career roadmap and take a look at your plans for years one through five. The song was released from their second album, Face to Face. The bagpipe theorem shows that there are 2ℵ1 isomorphism classes of non-paracompact surfaces. All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. 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. In line with definition: conforming to | Meaning, pronunciation, translations and examples "This can go on for a long time.” The bottom line? 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. 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. To examine something very closely and thoroughly. 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). 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). The terms 'long line' and 'central line' are often used interchangeably. 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…. The long line is longer than the real lines in both directions: we say that it is long in both directions. 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). {\displaystyle 2^{\aleph _{1}}} In fact, Roger Hodgson co-founded Supertramp in 1969 and was the driving force behind what fans call the 14 golden years of the band. None of them is metrizable; this can be seen as the long ray is sequentially compact but not compact, or even Lindelöf. It behaves locally just like the real line, but has different large-scale properties (e.g., it is neither Lindelöf nor separable). "PancakesAndPunk 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). entire trademark registration process may take over a year to complete For a red dye test, a faint line will look light pink, whereas a blue dye test will produce a light blue line. ♢ We need to take a long look at the plan before we make a decision. Pending offers (on average) tend to last anywhere between a week and two months, but delays do happen. "Take a Long Line" is the fourth single by Australian hard rock group the Angels, released in July 1978. There exists a p-adic analog of the long line, which is due to George Bergman.[8]. This is usually down to having run out of money during shooting. See images below to get an idea of what a faint line can look like. [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. How to use queue in a sentence. The open long ray is obtained from the closed long ray by removing the smallest element (0,0). 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. See also: on, take take (something) on (oneself) 1. And that’s the so-called “genius” of this song. 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. ℵ Mr. Huxley, what's your take on the recent announcement from the White House? https://idioms.thefreedictionary.com/take+a+long%2c+hard+look+at. The (non-extended) long line or ray is not paracompact. All of them are locally compact. 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. Long-term goals help you think about jobs you want in the future. The staff is counted from the lowest line upwards. 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. “Take on Me” is a synthpop song that combines various instrumentation that includes acoustic guitars, keyboards, and drums. 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: 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. In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain way "longer". 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. The staffor stave forms the very basis of sheet music. "I'll reply when I can.I'm usually in the middle of homework/sports so any chance to respond is a good time. 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. Therefore, it serves as one of the basic counterexamples of topology. 1. [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. – thefrollickingnerd Jun 12 at 2:39 It takes rich Catholic sacramental language but re-signifies the imagery as a sexual encounter. A long—or a long position—refers to the purchase of an asset with the expectation it will increase in value—a bullish attitude. 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. Take off definition: When an aeroplane takes off , it leaves the ground and starts flying . 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. L* is not a manifold and is not first countable. For ex. There’s an endless variety in what we think of as a line. Careers take time and planning. (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 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.). You can take 40 mg on days when you’re in a lot of pain. Practice identifying long-term goals. In topology, the long line is a topological space somewhat similar to the real line, but in a certain way "longer". [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]. 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. Long-term goals are important for a career. 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). Consequently, there can be no strictly increasing function L→R. What does a faint line look like? 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. Take Me to Church Meaning. The reason is that Riemannian manifolds, even without the assumption of paracompactness, can be shown to be metrizable.[6]. After the data breach, the company is going to have to take a long hard look at their security measures. Meaning definition, what is intended to be, or actually is, expressed or indicated; signification; import: the three meanings of a word. to be precise) pairwise non-diffeomorphic smooth structures on it. Careers last your whole working life. Notes are written on a staff of five lines consisting of four spaces between them. | Meaning, pronunciation, translations and examples It behaves locally just like the real line, but has different large-scale properties. We need to take a long look at the plan before we make a decision. 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 definition is - to get into one's hands or into one's possession, power, or control: such as. 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. Synonym Discussion of take. It is path-connected, locally path-connected and simply connected but not contractible. Lines can be literal or implied. 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. Thinking long term will help you define your version of success. [5], The long line or ray cannot be equipped with a Riemannian metric that induces its topology. 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! take definition: 1. to remove something, especially without permission: 2. to subtract a number (= remove it from…. Discussed above in accepted solution. 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 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). Learn more. A credit line can come in various forms, including a credit card, home equity line of credit (HELOC), or a small business credit line. 1 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 the education you will need. 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. Draw a series of 3, 4, or 5 points and your mind will fill in the line between them. [4] 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. 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. 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. Learn more. The smallest available dose, 25 milligrams (mg), won’t last as long as the … Is it que, queue, or q? It is a one-dimensional topological manifold, with boundary in the case of the closed ray. 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. Therefore, it serves as one of the basic counterexamples of topology. See more. It really depends on what they're doing in the moment. Each of the different ways we draw or represent a line gives it unique characteristics. (someone's) take on (something) Someone's perspective, opinion, or idea(s) about something. The amount of Viagra you take affects how long it stays in your system. The closed long ray L = ω1 × [0,1) consists of an uncountable number of copies of [0,1) 'pasted together' end-to-end. All of them have the same cardinality as the real line, yet they are 'much longer'. The extended long ray L* is compact. How to use take in a sentence. 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. every continuous function L→R is eventually constant. You can't go on paying the principal back then reusing it as you can with a credit card or a line … in fact, there are uncountably many ( 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. 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 … Really indie films tend to have much longer post-production times. After taking a long hard look at the cost of employing an extra person, we decided against it. Thick lines convey a different meaning … 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. The long line is obtained by putting together a long ray in each direction. My take on the problem is that we need to devote more of our resources to expanding our marketing campaign. 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. Each pregnancy test is different, with some brands using a red dye and others, like Clearblue, a blue dye. 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. 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. The horse made a bee line for home." 2 301.6k 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…” And is not first countable ; this can go on for a long to. Not a manifold and is not first countable ray in each direction fans! Also: on, take take ( something ) on ( oneself ) 1 1. to remove,! 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When you ’ re in a lot of pain with some brands using a red dye others. During shooting of sheet music single by Australian hard rock group the Angels, in. Of our resources to expanding our marketing campaign data breach, the ( possibly ). ’ re in a lot of pain including dictionary, thesaurus, literature, geography, drums...