A NOTE ON SPACES DETERMINED BY CLOSURE-LIKE OPERATORS

- Journal title : East Asian mathematical journal
- Volume 32, Issue 3, 2016, pp.365-375
- Publisher : Youngnam Mathematical Society
- DOI : 10.7858/eamj.2016.027

Title & Authors

A NOTE ON SPACES DETERMINED BY CLOSURE-LIKE OPERATORS

Hong, Woo Chorl; Kwon, Seonhee;

Hong, Woo Chorl; Kwon, Seonhee;

Abstract

In this paper, we study some classes of spaces determined by closure-like operators , and etc. which are wider than the class of 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 k-space is countably sequential and obtain that X is a WACP and weakly k-space iff X is sequential as a corollary.

Keywords

sequential;;countable tightness;k-space;AP;WAP;WACP;WADS;countably sequential;

Language

English

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