Browse > Article
http://dx.doi.org/10.4134/JKMS.2007.44.4.845

CONVERGENCE PROPERTIES OF HYPERSPACES  

Maio, Giuseppe Di (DIPARTIMENTO DI MATEMATICA SECONDA UNIVERSITY)
Kocinac, Lj. D. R. (FACULTY OF SCIENCES AND MATHEATICS UNIVERSITY OF NIS)
Nogura, Tsugunori (FACULTY OF SCIENCES EHIME UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.4, 2007 , pp. 845-854 More about this Journal
Abstract
In this paper we investigate relationships between closure-type and convergence-type properties of hyperspaces over a space X and covering properties of X.
Keywords
selection principles; hyperspace; ${\omega}$-cover; k-cover; ${\gamma}$-cover; ${\gamma}k$-cover; filter-$Fr\acute{e}chet$; strongly filter-$Fr\acute{e}chet$; set-$Fr\acute{e}chet$; strongly set-$Fr\acute{e}chet$; ${\alpha}_i$-properties;
Citations & Related Records

Times Cited By Web Of Science : 5  (Related Records In Web of Science)
Times Cited By SCOPUS : 4
연도 인용수 순위
1 Lj. D. R. Combinatorics of open covers VII: Groupability, Fund. Math. 179 (2003), no. 2, 131-155   DOI
2 V. I. Malyhin, The tightness and Suslin number in exp X and in a product of spaces, Soviet Math. Dokl. 13 (1972), 496-499
3 A. V. Arhangel'skii and T. Nogura, Relative sequentiality, Topology Appl. 82 (1998), no. 1-3, 49-58   DOI   ScienceOn
4 Lj. D. R. Kocinac, ${\gamma}-sets,\;{\gamma}_k-sets$ and hyperspaces, Math. Balkanica 19 (2005), 109-118
5 Lj. D. R. Kocinac and M. Scheepers, Function spaces and a property of Reznichenko, Topology Appl. 123 (2002), no. 1, 135-143   DOI   ScienceOn
6 G. Di Maio, E. Meccariello, and S. Naimpally, Unijormizing (proximal) ${\Delta}-topologies$, Topology Appl. 137 (2004), no. 1-3, 99-113   DOI   ScienceOn
7 A. V. Arhangel'skii, Frequency spectrum of a topological space and classification of spaces, Soviet Math. Dokl. 13 (1972), 1185-1189
8 C. Costantini, L. Hola and P. Vitolo, Tightness, character and related properties of hyperspace topologies, Topology Appl. 142 (2004), no. 1-3, 245-292   DOI   ScienceOn
9 G. Di Maio, Lj. D. R. Kocinac, and E. Meccariello, Selection principles and hyperspace topologies, Topology Appl. 153 (2005), no. 5-6, 912-923   DOI   ScienceOn
10 R. Engelking, General Topology, Heldermann, Berlin, 1989
11 J. M. G. Fell, A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff spaces, Proc. Amer. Math. Soc. 13 (1962), 472-476   DOI   ScienceOn
12 J. Gerlits and Zs. Nagy, Some properties of C(X), I, Topology Appl. 14 (1982), no. 2, 151-161   DOI   ScienceOn
13 K. Kunen, A compact L-space under CH, Topology Appl. 12 (1981), no. 3, 283-287   DOI   ScienceOn
14 J .-C. Hou, Character and tightness of hyperspaces with the Fell topology, Topology Appl. 84 (1998), no. 1-3. 199-206   DOI   ScienceOn
15 W. Just, A. W. Miller, M. Scheepers, and P. J. Szeptycki, Combinatorics of open covers II, Topology Appl. 73 (1996), no. 3, 241-266   DOI   ScienceOn
16 Lj. D. R. Kocinac, The Reznichenko property and the Pytkeev property in hyperspaces, Acta Math. Hungar. 107 (2005), no. 3, 225-233   DOI
17 T. Nogura, The product of $<{\alpha}_i>$-spaces, Topology Appl. 21 (1985), no. 3, 251-259   DOI   ScienceOn
18 T. Nogura, D. Shakhmatov, and Y. Tanaka, ${\alpha}_4-property$ versus A-property in topological spaces and groups, Stud. Sci. Math. Hungar. 33 (1997), no. 4, 351-362
19 H. Poppe, Eine Bemerkung uber Trennungsaxiome in Raumen von abgeschlossenen Teilmengen topologisher Raume, Arch. Math. 16 (1965), 197-199   DOI
20 M. Sakai, The sequence selection properties of $C_p$(X), Topology Appl., to appear
21 M. Scheepers, Combinatorics of open covers I: Ramsey theory, Topology Appl. 69 (1996), no. 1, 31-62   DOI   ScienceOn
22 M. Scheepers, $C_p$(X) and Arhangel'skii's ${\alpha}_i$-spaces, Topology Appl. 89 (1998), no. 3, 265-275   DOI   ScienceOn
23 D. B. Shakhmatov, ${\alpha}_i-properties$ in Frechet- Urysohn topological groups, Topology Proc. 15 (1990), 143-183