# A NOTE ON SPACES WHICH HAVE COUNTABLE TIGHTNESS

Hong, Woo-Chorl

• Accepted : 2010.11.25
• Published : 2011.04.30
• 28 3

#### 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$\'{e}$chet-Urysohn property which is equivalent to countable tightness.

#### Keywords

countable tightness;c(a)-closure operators;strongly sequentially closed;strongly sequentially open;weak Fr$\'{e}$chet-Urysohn property

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#### Cited by

1. ON SPACES WHICH HAVE COUNTABLE TIGHTNESS AND RELATED SPACES vol.34, pp.2, 2012, https://doi.org/10.5831/HMJ.2012.34.2.199