Abstract
A topological space X is called CC-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 countably compact subspace A subset of X. A topological space X is called CC2-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 countably compact subspace A subset of X. We investigate these two properties.