ON SPACES IN WHICH COMPACT-LIKE SETS ARE CLOSED, AND RELATED SPACES

- Journal title : Communications of the Korean Mathematical Society
- Volume 22, Issue 2, 2007, pp.297-303
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2007.22.2.297

Title & Authors

ON SPACES IN WHICH COMPACT-LIKE SETS ARE CLOSED, AND RELATED SPACES

Hong, Woo-Chorl;

Hong, Woo-Chorl;

Abstract

In this paper, we study on C-closed spaces, SC-closed spaces and related spaces. We show that a sequentially compact SC-closed space is sequential and as corollaries obtain that a sequentially compact space with unique sequential limits is sequential if and only if it is C-closed [7, 1.19 Proposition] and every sequentially compact SC-closed space is C-closed. We also show that a countably compact WAP and C-closed space is sequential and obtain that a countably compact (or compact or sequentially compact) WAP-space with unique sequential limits is sequential if and only if it is C-closed as a corollary. Finally we prove that a weakly discretely generated AP-space is C-closed. We then obtain that every countably compact (or compact or sequentially compact) weakly discretely generated AP-space is -Urysohn with unique sequential limits, for weakly discretely generated AP-spaces, unique sequential limits , and every continuous surjective function from a countably compact (or compact or sequentially compact) space onto a weakly discretely generated AP-space is closed as corollaries.

Keywords

KC;C-closed;SC-closed;-Urysohn;sequential;AP;WAP;weakly discretely generated;

Language

English

Cited by

1.

ON SPACES IN WHICH THE THREE MAIN KINDS OF COMPACTNESS ARE EQUIVALENT,;

1.

2.

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