On complete accumulation points of discrete subsets

Abstract

Abstract. We introduce a class of spaces in which every discrete subset has a complete accumulation point. Properties of this class are obtained and consistent examples are given to show that this class differs from the class of countably compact and the class of compact spaces. A number of questions are posed. AMS Classification:Primary 54A25, 54A35, 54D99

Dually discrete spaces

“…Recall from [1] that a space X is discretely complete if every discrete subspace of X has a complete accumulation point in X . Clearly every compact T 1 -space is discretely complete and every discretely complete space is countably compact.…”