A Note on Spaces Determined by Closure-Like Operators

Abstract

Abstract. In this paper, we study some classes of spaces determined by closure-like operators [·]s, [·]c and [·] k etc. which are wider than the class of Fréchet-Urysohn spaces or the class of sequential spaces and related spaces. We first introduce a WADS space which is a generalization of a sequential space. We show that X is a WADS and k-space iff X is sequential and every WADS space is C-closed and obtained that every WADS and countably compact space is sequential as a corollary. We also show that every WAP and countably compact space is countably sequential and obtain that every WACP and countably compact space is sequential as a corollary. And we show that every WAP and weakly kspace is countably sequential and obtain that X is a WACP and weakly k-space iff X is sequential as a corollary.