Abstract
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 vertical bar(A) : A -> f(A) is a homeomorphism for each compact subspace A subset of X. A topological space X is called C-2- paracompact if there exist a Hausdorff paracompact space Y and a bijective function f : X -> Y such that the restriction f vertical bar(A) : A -> f (A) is a homeomorphism for each compact subspace A subset of X . We investigate these two properties and produce some examples to illustrate the relationship between them and C-normality, minimal Hausdorff, and other properties.