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Paracompact Space


A paracompact space is a T2-space such that every open cover has a locally finite open refinement. Paracompactness is a very common property that topological spaces satisfy. Paracompactness is similar to the compactness property, but generalized for slightly "bigger" spaces. All manifolds (e.g, second countable and T2-spaces) are paracompact.


See also

Compact Space, Locally Finite Space, Manifold, Second Countable Space, T2-Space, Topological Space

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Cite this as:

Weisstein, Eric W. "Paracompact Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ParacompactSpace.html

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