Moore space (topology) | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-03-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Moore_space_(topology)


00:01:04 Examples and properties
00:02:52 Normal Moore space conjecture



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SUMMARY
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In mathematics, more specifically point-set topology, a Moore space is a developable regular Hausdorff space. Equivalently, a topological space X is a Moore space if the following conditions hold:

Any two distinct points can be separated by neighbourhoods, and any closed set and any point in its complement can be separated by neighbourhoods. (X is a regular Hausdorff space.)
There is a countable collection of open covers of X, such that for any closed set C and any point p in its complement there exists a cover in the collection such that every neighbourhood of p in the cover is disjoint from C. (X is a developable space.)Moore spaces are generally interesting in mathematics because they may be applied to prove interesting metrization theorems. The concept of a Moore space was formulated by R. L. Moore in the earlier part of the 20th century.