V.V. Tkachuk, I.V. Yaschenko
Almost closed sets and topologies they determine

Comment.Math.Univ.Carolinae 42,2 (2001) 395-405.

Abstract:We prove that every countably compact AP-space is Fr\'echet-Urysohn. It is also established that if $X$ is a paracompact space and $C_p(X)$ is AP, then $X$ is a Hurewicz space. We show that every scattered space is WAP and give an example of a hereditarily WAP-space which is not an AP-space.

Keywords: AP-space, WAP-space, scattered space, countably compact space, function space, discretely generated space
AMS Subject Classification: 54A25, 54D55