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http://dx.doi.org/10.5831/HMJ.2015.37.4.549

STRONG VERSIONS OF κ-FRÉCHET AND κ-NET SPACES  

CHO, MYUNG HYUN (Department of Mathematics Education Wonkwang University)
KIM, JUNHUI (Department of Mathematics Education Wonkwang University)
MOON, MI AE (Division of Mathematics & Informational Statistics Wonkwang University)
Publication Information
Honam Mathematical Journal / v.37, no.4, 2015 , pp. 549-557 More about this Journal
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;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 A. V. Arhangel'skii and V. I. Ponomarev, Fundamentals of General Topology, D. Reidel Publishing Co., Dordrecht/Boston/Lancaster, 1984.
2 M.H. Cho, J. Kim, and M.A. Moon, Generalized properties of strongly Frechet, Honam Math. J., 34(1) (2012), 85-92.   DOI
3 M.H. Cho, M. A. Moon, and J. Kim, New cardinal functions related to almost closed sets, Honam Math. J., 35(3) (2013), 541-550.   DOI
4 R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.
5 R. E. Hodel, A theory of convergence and cluster points based on $\kappa$-nets, Topology Proc., 35 (2010), 291-330.
6 A. Kaminski, Remarks on multivalued convergence, in: J. Novak(Ed.), General Topology and its Relations to Modern Analysis Algebra V, Proc. Fifth Prague Topol. Symp., 1981, 418-422, Heldermann Verlag, Berlin, 1982.
7 P. R. Meyer, Sequential properties of ordered topological spaces, Compositio Mathematicae, 21 (1969), 102-106.
8 E. Michael, A quintuple quotient quest, Gen. Topology Appl., 2 (1972), 91-138.   DOI