Topological space | Wikipedia audio article
Channel: wikipedia tts
Date: 27/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Topological_space


00:00:56 1 History
00:03:34 2 Definition
00:04:06 2.1 Definition via neighbourhoods
00:06:19 2.2 Definition via open sets
00:07:01 2.2.1 Examples
00:07:10 2.3 Definition via closed sets
00:07:35 2.4 Other definitions
00:08:00 3 Comparison of topologies
00:08:23 4 Continuous functions
00:08:42 5 Examples of topological spaces
00:09:30 5.1 Metric spaces
00:10:17 5.2 Proximity spaces
00:11:24 5.3 Uniform spaces
00:11:39 5.4 Function spaces
00:11:49 5.5 Cauchy spaces
00:13:04 5.6 Convergence spaces
00:13:16 5.7 Grothendieck sites
00:14:09 5.8 Other spaces
00:15:33 6 Topological constructions
00:15:47 7 Classification of topological spaces
00:16:03 8 Topological spaces with algebraic structure
00:16:18 9 Topological spaces with order structure
00:16:38 10 See also
00:16:53 11 Notes
00:17:15 12 References
00:19:47 13 External links
00:20:00 Topological constructions
00:22:22 Classification of topological spaces
00:23:07 Topological spaces with algebraic structure
00:23:49 Topological spaces with order structure
00:24:19 See also



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SUMMARY
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In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods. The definition of a topological space relies only upon set theory and is the most general notion of a mathematical space that allows for the definition of concepts such as continuity, connectedness, and convergence. Other spaces, such as manifolds and metric spaces, are specializations of topological spaces with extra structures or constraints. Being so general, topological spaces are a central unifying notion and appear in virtually every branch of modern mathematics. The branch of mathematics that studies topological spaces in their own right is called point-set topology or general topology.