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
Famous quotes containing the word space:
“In the tale proper—where there is no space for development of character or for great profusion and variety of incident—mere construction is, of course, far more imperatively demanded than in the novel.”
—Edgar Allan Poe (1809–1849)