Year: 2011
Type: article
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.
Author: Woo-Chorl Hong
Institution: Pusan National University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: Pusan National University
OpenAlex ID: W2009403891