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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“The within, all that inner space one never sees, the brain and the heart and other caverns where thought and feeling dance their sabbath.”
—Samuel Beckett (1906–1989)