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

### 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 ...

### Famous quotes containing the word space:

“For good teaching rests neither in accumulating a shelfful of knowledge nor in developing a repertoire of skills. In the end, good teaching lies in a willingness to attend and care for what happens in our students, ourselves, and the *space* between us. Good teaching is a certain kind of stance, I think. It is a stance of receptivity, of attunement, of listening.”

—Laurent A. Daloz (20th century)