# 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
• 35 8

#### 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