Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A NOTE ON SPACES WHICH HAVE COUNTABLE TIGHTNESS

  • Hong, Woo-Chorl (Department of Mathematics Education Pusan National University)
  • Received : 2010.01.11
  • Accepted : 2010.11.25
  • Published : 2011.04.30
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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.

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References

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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