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A paracompact space is a Hausdorff 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 Hausdorff) are paracompact.
See also Hausdorff Space, Locally Finite Space, Manifold, Topological Space