CONVERGENCE PROPERTIES OF HYPERSPACES

Title & Authors
CONVERGENCE PROPERTIES OF HYPERSPACES
Maio, Giuseppe Di; Kocinac, Lj. D. R.; Nogura, Tsugunori;

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;$\small{{\omega}}$-cover;k-cover;$\small{{\gamma}}$-cover;$\small{{\gamma}k}$-cover;filter-$\small{Fr\acute{e}chet}$;strongly filter-$\small{Fr\acute{e}chet}$;set-$\small{Fr\acute{e}chet}$;strongly set-$\small{Fr\acute{e}chet}$;$\small{{\alpha}_i}$-properties;
Language
English
Cited by
1.
Some covering properties of hyperspaces, Topology and its Applications, 2008, 155, 17-18, 1959
2.
Selection principles, γ-sets and αi-properties in Čech closure spaces, Topology and its Applications, 2008, 155, 17-18, 1947
3.
Statistical convergence in topology, Topology and its Applications, 2008, 156, 1, 28
References
1.
﻿A. V. Arhangel'skii, Frequency spectrum of a topological space and classification of spaces, Soviet Math. Dokl. 13 (1972), 1185-1189

2.
﻿A. V. Arhangel'skii and T. Nogura, Relative sequentiality, Topology Appl. 82 (1998), no. 1-3, 49-58

3.
﻿C. Costantini, L. Hola and P. Vitolo, Tightness, character and related properties of hyperspace topologies, Topology Appl. 142 (2004), no. 1-3, 245-292

4.
G. Di Maio, Lj. D. R. Kocinac, and E. Meccariello, Selection principles and hyperspace topologies, Topology Appl. 153 (2005), no. 5-6, 912-923

5.
G. Di Maio, E. Meccariello, and S. Naimpally, Unijormizing (proximal) ${\Delta}-topologies$, Topology Appl. 137 (2004), no. 1-3, 99-113

6.
R. Engelking, General Topology, Heldermann, Berlin, 1989

7.
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

8.
﻿J. Gerlits and Zs. Nagy, Some properties of C(X), I, Topology Appl. 14 (1982), no. 2, 151-161

9.
﻿J .-C. Hou, Character and tightness of hyperspaces with the Fell topology, Topology Appl. 84 (1998), no. 1-3. 199-206

10.
﻿W. Just, A. W. Miller, M. Scheepers, and P. J. Szeptycki, Combinatorics of open covers II, Topology Appl. 73 (1996), no. 3, 241-266

11.
﻿Lj. D. R. Kocinac, The Reznichenko property and the Pytkeev property in hyperspaces, Acta Math. Hungar. 107 (2005), no. 3, 225-233

12.
Lj. D. R. Kocinac, ${\gamma}-sets,\;{\gamma}_k-sets$ and hyperspaces, Math. Balkanica 19 (2005), 109-118

13.
Lj. D. R. Kocinac and M. Scheepers, Function spaces and a property of Reznichenko, Topology Appl. 123 (2002), no. 1, 135-143

14.
Lj. D. R. Combinatorics of open covers VII: Groupability, Fund. Math. 179 (2003), no. 2, 131-155

15.
﻿K. Kunen, A compact L-space under CH, Topology Appl. 12 (1981), no. 3, 283-287

16.
V. I. Malyhin, The tightness and Suslin number in exp X and in a product of spaces, Soviet Math. Dokl. 13 (1972), 496-499

17.
﻿T. Nogura, The product of $<{\alpha}_i>$-spaces, Topology Appl. 21 (1985), no. 3, 251-259

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

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

22.
M. Scheepers, $C_p$(X) and Arhangel'skii's ${\alpha}_i$-spaces, Topology Appl. 89 (1998), no. 3, 265-275

23.
D. B. Shakhmatov, ${\alpha}_i-properties$ in Frechet- Urysohn topological groups, Topology Proc. 15 (1990), 143-183