Moore Space (topology)

Moore Space (topology)

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.

Read more about Moore Space (topology):  Examples and Properties, Normal Moore Space Conjecture

Other articles related to "moore":

Moore Space (topology) - Normal Moore Space Conjecture
... For a long time, topologists were trying to prove the so-called normal Moorespace conjecture every normal Moorespace is metrizable ... was inspired by the fact that all known Moorespaces that were not metrizable were also not normal ... implies that locally compact, normal Moorespaces are metrizable ...

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