COUNTABLE NORMALITY

A topological space X is called countably normal if there exist a normal 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 countable subspace A subset of X. We will investigate this property and produce some examples to illustrate the relationship between countable normality and other weaker kinds of normality. We answer the following open problem of Arhangel'skii : "Is there a Tychonoff space which is not C-normal?".