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 Space:  Paracompactness, Examples, Properties, Paracompact Hausdorff Spaces, Relationship With Compactness, Variations

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