Paracompact Space

In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by Dieudonné (1944). The notion of paracompactness generalizes ordinary compactness; a key motivation for the notion of paracompactness is that it is a sufficient condition for the existence of partitions of unity.

A hereditarily paracompact space is a space such that every subspace of it is a paracompact space. This is equivalent to requiring that every open subspace be paracompact.

Read more about Paracompact SpaceParacompactness, Examples, Properties, Paracompact Hausdorff Spaces, Relationship With Compactness, Variations

Other articles related to "paracompact space, space":

Paracompact Space - Variations - Definition of Relevant Terms For The Variations
... A star refinement of a cover of a space X is a new cover of the same space such that, given any point in the space, the star of the point in the new cover is a subset of some set in ... A cover of a space X is pointwise finite if every point of the space belongs to only finitely many sets in the cover ... As the name implies, a fully normal space is normal ...

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