East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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A NOTE ON SPACES DETERMINED BY CLOSURE-LIKE OPERATORS

  • Hong, Woo Chorl (Department of Mathematics Education, Pusan National University) ;
  • Kwon, Seonhee (Department of Mathematics, University of Ulsan)
  • Received : 2016.02.25
  • Accepted : 2016.04.21
  • Published : 2016.05.31
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Abstract

In this paper, we study some classes of spaces determined by closure-like operators $[{\cdot}]_s$, $[{\cdot}]_c$ and $[{\cdot}]_k$ etc. which are wider than the class of $Fr{\acute{e}}chet-Urysohn$ spaces or the class of sequential spaces and related spaces. We first introduce a WADS space which is a generalization of a sequential space. We show that X is a WADS and k-space iff X is sequential and every WADS space is C-closed and obtained that every WADS and countably compact space is sequential as a corollary. We also show that every WAP and countably compact space is countably sequential and obtain that every WACP and countably compact space is sequential as a corollary. And we show that every WAP and weakly k-space is countably sequential and obtain that X is a WACP and weakly k-space iff X is sequential as a corollary.

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References

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