A NOTE ON SPACES DETERMINED BY CLOSURE-LIKE OPERATORS
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In this paper, we study some classes of spaces determined byclosure-like operators [·]s, [·]c and [·]k etc. which are wider than the classof Fréchet-Urysohn spaces or the class of sequential spaces and relatedspaces. We first introduce a WADS space which is a generalization ofa sequential space. We show that X is a WADS and k-space iff X issequential and every WADS space is C-closed and obtained that everyWADS and countably compact space is sequential as a corollary. Wealso show that every WAP and countably compact space is countablysequential and obtain that every WACP and countably compact space issequential as a corollary. And we show that every WAP and weakly k-space is countably sequential and obtain that X is a WACP and weaklyk-space iff X is sequential as a corollary.
Abstract
In this paper, we study some classes of spaces determined byclosure-like operators [ ]s, [ ]c and [ ]k etc. which are wider than the classof Fr echet-Urysohn spaces or the class of sequential spaces and relatedspaces. We rst introduce a WADS space which is a generalization ofa sequential space. We show that X is a WADS and k-space i X issequential and every WADS space is C-closed and obtained that everyWADS and countably compact space is sequential as a corollary. Wealso show that every WAP and countably compact space is countablysequential and obtain that every WACP and countably compact space issequential as a corollary. And we show that every WAP and weakly k-space is countably sequential and obtain that X is a WACP and weaklyk-space i X is sequential as a corollary.
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