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The Chicken Dance is an example of a line dance adopted by the Mod revival during the 1980s. [18] The music video for the 1990 Billy Ray Cyrus song "Achy Breaky Heart" has been credited for launching line dancing into the mainstream. [2] [19] [20] [21] In the 1990s, the hit Spanish dance song "Macarena" inspired a popular line dance. [22]
Extended real number line; Fake 4-ball − A compact contractible topological 4-manifold. House with two rooms − A contractible, 2-dimensional simplicial complex that is not collapsible. Klein bottle; Lens space; Line with two origins, also called the bug-eyed line − It is a non-Hausdorff manifold.
Tychonoff plank – the topological product of the two ordinal spaces [,] and [,], where is the first infinite ordinal and the first uncountable ordinal; Long line (topology) – a generalization of the real line from a countable number of line segments [0, 1) laid end-to-end to an uncountable number of such segments.
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A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
For example, the real line is Tychonoff under the standard Euclidean topology. Other examples include: Every metric space is Tychonoff; every pseudometric space is completely regular. Every locally compact regular space is completely regular, and therefore every locally compact Hausdorff space is Tychonoff.
In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), [2] [3] also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.
Let the real line have its standard topology. Then every open subset of the real line is a countable union of open intervals. Generalized Statement