[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7858/eamj.2016.027

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)

Publication Information

East Asian mathematical journal / v.32, no.3, 2016 , pp. 365-375 More about this Journal

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.

Keywords

sequential; $Fr{\acute{e}}chet-Urysohn$ ; countable tightness; k-space; AP; WAP; WACP; WADS; countably sequential;

Citations & Related Records

Times Cited By KSCI : 5 (Citation Analysis)

Reference
Cited By KSCI

1	A. V. Arhangel'skii, A characterization of very k-spaces, Czechoslovak Math. J. 18(93)(1968), 392-395.
2	A. V. Arhangel'skii and L.S.Pontryagin(Eds.), General Topology I, Encyclopaedia of Mathematical Sciences, vol. 17, Springer-Verlage, Berlin, 1990.
3	A. V. Arhangel'skii, Topological function spaces, Mathematics and its application, Vol.78, Kluwer Academic Publishers, 1992.
4	A. V. Arhangel'skii and D. N. Stavrova, On a common generalization of k-spaces and spaces with countable tightness, Top. and its Appl. 51(1993), 261-268. DOI
5	A. Bella, On spaces with the property of weak approximation by points, Comment. Math. Univ. Carolinae 35(2)(1994), 357-360.
6	A. Bella and I. V. Yaschenko, On AP andWAP spaces, Comment. Math. Univ. Carolinae 40(3)(1999), 531-536.
7	A. Dow, M. G. Tkachenko, V. V. Tkachuk and R. G .Wilson, Topologies generated by discrete subspaces, Glansnik Math. 37(57)(2002), 187-210.
8	S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57(1965), 107-115. DOI
9	W. C. Hong, Generalized Frechet-Urysohn spaces, J. Korean Math. Soc. 44(2)(2007), 261-273. DOI
10	W. C. Hong, On spaces in which compact-like sets are closed, and related spaces, Commun. Korean Math. Soc. 22(2)(2007), 297-303. DOI
11	W. C. Hong, On spaces which have countable tightness and related spaces, Honam Math. J. 34(2)(2012), 199-208. DOI
12	W. C. Hong and S. Kwon, A generalization of a sequential space and related spaces, Honam Math. J. 36(2)(2014), 425-434. DOI
13	M. Ismail and P. Nyikos, On spaces in which countably compact sets are closed, and hereditary properties, Top. and its Appl. 11(1980), 281-292. DOI
14	S. Lin and C. Zheng, The k-quotient images of metric spaces, Commun. Korean Math. Soc. 27(2012), 377-384. DOI
15	M. A. Moon, M. H. Cho and J. Kim, On AP spaces in concern with compact-like sets and submaximality, Comment. Math. Univ. Carolinae 52(2)(2011), 293-302.
16	J. Pelant, M. G. Tkachenko, V. V. Tkachuk and R. G. Wilson, Pseudocompact Whyburn spaces need not be Frechet, Proc. Amer. Math. Soc. 131(2003), no.10,3257-3265. DOI
17	Y. Tanaka, Necessary and sufficient conditions for products of k-spaces, Top. Proceedings 14(1989), 281-313.
18	V. V. Tkachuk and I. V. Yaschenko, Almost closed sets and topologies they determine, Comment. Math. Univ. Carolinae 42(2)(2001), 395-405.
19	A. Wilansky, Topology for analysis, Ginn and Company 1970.