Moore space (topology)

In mathematics, more specifically point-set topology, a Moore space is a developable regular Hausdorff space. That is, 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.