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http://dx.doi.org/10.4134/JKMS.2007.44.2.261

GENERALIZED FRÉCHET-URYSOHN SPACES  

Hong, Woo-Chorl (Department of Mathematics Education Pusan National University)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.2, 2007 , pp. 261-273 More about this Journal
Abstract
In this paper, we introduce some new properties of a topological space which are respectively generalizations of $Fr\-Urysohn property. We show that countably AP property is a sufficient condition for a space being countable tightness, sequential, weakly first countable and symmetrizable, to be ACP, $Fr\, first countable and semimetrizable, respectively. We also prove that countable compactness is a sufficient condition for a countably AP space to be countably $Fr\. We then show that a countably compact space satisfying one of the properties mentioned here is sequentially compact. And we show that a countably compact and countably AP space is maximal countably compact if and only if it is $Fr\. We finally obtain a sufficient condition for the ACP closure operator $[{\cdot}]_{ACP}$ to be a Kuratowski topological closure operator and related results.
Keywords
$Fr\; sequential; countably $Fr\; countable tightness; AP; countably AP; WAP; ACP; WACP; countably compact;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 6
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