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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“Thus all our dignity lies in thought. Through it we must raise ourselves, and not through space or time, which we cannot fill. Let us endeavor, then, to think well: this is the mainspring of morality.”
—Blaise Pascal (1623–1662)