Weight of a topological space | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-04

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Base_(topology)


00:00:29 1 Definition and basic properties
00:03:47 2 Objects defined in terms of bases
00:04:31 3 Theorems
00:06:11 4 Base for the closed sets
00:08:01 5 Weight and character
00:09:52 5.1 Increasing chains of open sets
00:13:04 6 See also
00:14:25 7 Notes
00:14:45 8 References



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SUMMARY
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In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in X such that every open set in X can be written as a union of elements of B. We say that the base generates the topology T. Bases are useful because many properties of topologies can be reduced to statements about a base generating that topology, and because many topologies are most easily defined in terms of a base which generates them.