Relatively Absolutely Countably Compact Spaces

A subspace Y of a space X is absolutely countably compact(=acc) (strongly absolutely countably compact(=strongly acc)) in X if for every open cover U of X and every dense subspace D subset of X (respectively, D subset of Y) there S exists a finite subset F subset of D such that Y subset of St(F, U), where St(F, U) = {U element of U : U intersection F ≠ ø}. In this paper, we investigate the relationships between these spaces and other starcompact spaces by giving some examples, and also study topological properties of relatively absolutely countably compact spaces.