A NOTE ON SPACES WHICH HAVE COUNTABLE TIGHTNESS

Title & Authors
A NOTE ON SPACES WHICH HAVE COUNTABLE TIGHTNESS
Hong, Woo-Chorl;

Abstract
In this paper, we introduce closure operators [$\small{{\cdot}}$]c and [$\small{{\cdot}}$]a on a space and study some relations among [$\small{{\cdot}}$]c, [$\small{{\cdot}}$]a and countable tightness. We introduce the concepts of a strongly sequentially closed set and a strongly sequentially open set and show that a space X has countable tightness if and only if every strongly sequentially closed set is closed if and only if every strongly sequentially open set is open. Finally we find a generalization of the weak Fr$\small{\$chet-Urysohn property which is equivalent to countable tightness.
Keywords
countable tightness;c(a)-closure operators;strongly sequentially closed;strongly sequentially open;weak Fr$\small{\$chet-Urysohn property;
Language
English
Cited by
1.
ON SPACES WHICH HAVE COUNTABLE TIGHTNESS AND RELATED SPACES,;

호남수학학술지, 2012. vol.34. 2, pp.199-208
1.
ON SPACES WHICH HAVE COUNTABLE TIGHTNESS AND RELATED SPACES, Honam Mathematical Journal, 2012, 34, 2, 199
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