A paracompact space is a T_2-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 T_2-spaces) are paracompact.

compact space | locally finite space | manifold | second countable space | T_2-space | topological space