A normal countably compact not absolutely countably compact space
by
Oleg Pavlov
Ohio University

A Hausdorff space X is called absolutely countably compact if for every open cover U of X and every dense F subset X there is finite G subset F such that St(U, G)=X. It is known that every compact space is absolutely countably compact and that every absolutely countably compact space is countably compact. It was shown recently by various authors that in many particular cases countable compactness implies absolute countable compactness. We present an example in the opposite direction, thus answering a question of A. V. Arhangel'skii.

Date received: February 5, 1998