The open long ray is obtained from the closed long ray by removing the smallest element (0,0). Refer to your career roadmap and take a look at your plans for years one through five. 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. 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. In fact, 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. 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. (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.). – thefrollickingnerd Jun 12 at 2:39 "PancakesAndPunk “Take on Me” is a synthpop song that combines various instrumentation that includes acoustic guitars, keyboards, and drums. every continuous function L→R is eventually constant. 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. 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 amount of Viagra you take affects how long it stays in your system. It was created by Michael Patterson and his wife Candace Reckinger, who would later work on videos for "Opposites Attract," "Luka" and "Impulsive. Draw a series of 3, 4, or 5 points and your mind will fill in the line between them. 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. The horse made a bee line for home." in fact, there are uncountably many ( For ex. The closed long ray L = ω1 × [0,1) consists of an uncountable number of copies of [0,1) 'pasted together' end-to-end. 1. See images below to get an idea of what a faint line can look like. 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: There exists a p-adic analog of the long line, which is due to George Bergman.[8]. After taking a long hard look at the cost of employing an extra person, we decided against it. [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]. It behaves locally just like the real line, but has different large-scale properties (e.g., it is neither Lindelöf nor separable). To examine something very closely and thoroughly. Consequently, there can be no strictly increasing function L→R. 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. Is it que, queue, or q? Each pregnancy test is different, with some brands using a red dye and others, like Clearblue, a blue dye. 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. 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. And that’s the so-called “genius” of this song. 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). Here are a … Learn more. Long-term goals help you think about jobs you want in the future. (someone's) take on (something) Someone's perspective, opinion, or idea(s) about something. Discussed above in accepted solution. Long-term goals help you think about the education you will need. Careers last your whole working life. It really depends on what they're doing in the moment. Queue definition is - a braid of hair usually worn hanging at the back of the head. 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. Lines can be literal or implied. 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. "This can go on for a long time.” The bottom line? The smallest available dose, 25 milligrams (mg), won’t last as long as the … It is a one-dimensional topological manifold, with boundary in the case of the closed ray. 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. 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. 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. See also: on, take take (something) on (oneself) 1. How to use take in a sentence. All of them are locally compact. (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.). If you think that kind of behavior is OK, you need to take a long hard look at your ethics. 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…” [4] The staff is counted from the lowest line upwards. 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. 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. 2 There’s an endless variety in what we think of as a line. 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. 1 {\displaystyle 2^{\aleph _{1}}} 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. 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. Thick lines convey a different meaning … 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). A credit line can come in various forms, including a credit card, home equity line of credit (HELOC), or a small business credit line. These plans will include your long-term goals. 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. "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. This is usually down to having run out of money during shooting. to be precise) pairwise non-diffeomorphic smooth structures on it. Pending offers (on average) tend to last anywhere between a week and two months, but delays do happen. Notes are written on a staff of five lines consisting of four spaces between them. 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. 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. As order topologies, the (possibly extended) long rays and lines are normal Hausdorff spaces. 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 … 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. Really indie films tend to have much longer post-production times. Synonym Discussion of take. Careers take time and planning. You can't go on paying the principal back then reusing it as you can with a credit card or a line … In line with definition: conforming to | Meaning, pronunciation, translations and examples 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). In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain way "longer". Meaning definition, what is intended to be, or actually is, expressed or indicated; signification; import: the three meanings of a word. Learn more. After the data breach, the company is going to have to take a long hard look at their security measures. 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. Take off definition: When an aeroplane takes off , it leaves the ground and starts flying . The (non-extended) long line or ray is not paracompact. 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. All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. 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