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.
Paracompact Space
See also
Compact Space, Locally Finite Space, Manifold, Second Countable Space, T2-Space, Topological SpaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Paracompact Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ParacompactSpace.html