STRONG VERSIONS OF κ-FRÉCHET AND κ-NET SPACES

• Journal title : Honam Mathematical Journal
• Volume 37, Issue 4,  2015, pp.549-557
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2015.37.4.549
Title & Authors
STRONG VERSIONS OF κ-FRÉCHET AND κ-NET SPACES
CHO, MYUNG HYUN; KIM, JUNHUI; MOON, MI AE;

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