A topological space X is called C-paracompact if there exist a paracompact space Y and a bijective function f:X Y such that the restriction f A:A f(A) is a homeomorphism for each compact subspace A⊆ X. A topological space X is called C₂-paracompact if there exist a Hausdorff paracompact space Y and a bijective function f:X Y such that the restriction f A:A f(A) is a homeomorphism for each compact subspace A⊆ X. We investigate these two properties and produce some examples to illustrate the relationship between them and C-normality, minimal Hausdorff, and other properties.
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Saeed et al. (2019) studied this question.