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STRONG VERSIONS OF κ-FRÉCHET AND κ-NET SPACES

  • CHO, MYUNG HYUN ;
  • KIM, JUNHUI ;
  • MOON, MI AE
  • Received : 2015.10.16
  • Accepted : 2015.12.07
  • Published : 2015.12.25

Abstract

We introduce strongly ${\kappa}$-$Fr{\acute{e}}chet$ and strongly ${\kappa}$-sequential spaces which are stronger than ${\kappa}$-$Fr{\acute{e}}chet$ and ${\kappa}$-net spaces respectively. For convenience, we use the terminology "${\kappa}$-sequential" instead of "${\kappa}$-net space", introduced by R.E. Hodel in [5]. And we study some properties and topological operations on such spaces. We also define strictly ${\kappa}$-$Fr{\acute{e}}chet$ and strictly ${\kappa}$-sequential spaces which are more stronger than strongly ${\kappa}$-$Fr{\acute{e}}chet$ and strongly ${\kappa}$-sequential spaces respectively.

Keywords

strongly $Fr{\acute{e}}chet$;${\kappa}$-net space;strongly ${\kappa}$-$Fr{\acute{e}}chet$;strongly ${\kappa}$-sequential;strictly ${\kappa}$-$Fr{\acute{e}}chet$;strictly ${\kappa}$-sequential

References

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Acknowledgement

Supported by : Wonkwang University