Separated space | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-03

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Hausdorff_space


00:00:38 1 Definitions
00:01:46 2 Equivalences
00:02:17 3 Examples and non-examples
00:02:25 4 Properties
00:03:58 5 Preregularity versus regularity
00:07:30 6 Variants
00:08:48 7 Algebra of functions
00:09:49 8 Academic humour
00:10:21 9 See also
00:10:51 10 Notes



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SUMMARY
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In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space where for any two distinct points there exists a neighbourhood of each which is disjoint from the neighbourhood of the other. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T2) is the most frequently used and discussed. It implies the uniqueness of limits of sequences, nets, and filters.
Hausdorff spaces are named after Felix Hausdorff, one of the founders of topology. Hausdorff's original definition of a topological space (in 1914) included the Hausdorff condition as an axiom.