Abstract
A C-paracompact is a topological space X associated with a paracompact space Y and a bijective function f : X -> Y satisfying that f up arrow(A): A -> f(A) is a homeomorphism for each compact subspace A subset of X. Furthermore, X is called C-2-paracompact if Y is T-2 paracompact. In this article, we discuss the above concepts and answer the problem of Arhangel'skii. Moreover, we prove that the sigma product Sigma(0) can not be condensed onto a T-2 paracompact space.