A note on spaces which have countable tightness
Commun. Korean Math. Soc. 2011 Vol. 26, No. 2, 297-304
https://doi.org/10.4134/CKMS.2011.26.2.297
Printed June 1, 2011
Woo Chorl Hong
Pusan National University
Abstract : In this paper, we introduce closure operators $[\cdot]_c$ and $[\cdot]_a$ on a space and study some relations among $[\cdot]_c$, $[\cdot]_a$ 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\'echet-Urysohn property which is equivalent to countable tightness.
Keywords : countable tightness, c(a)-closure operators, strongly sequentially closed, strongly sequentially open, and weak Fr\'echet-Urysohn property
MSC numbers : 54A20, 54B15, 54C10, 54D55, 54D99
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