VARIATIONS OF SEPARABILITY AND SUPERTIGHTNESS OF HYPERSPACES

Ritu Sen

DOI Number
https://doi.org/10.22190/FUMI230329017S
First page
247
Last page
263

Abstract


For a Hausdorff non-compact space X, relationships between closure-type properties of the hyperspace (Λ; τ∆+) and covering properties of that of X have been studied. We then investigate selective separability and some variations of this property. Finally supertightness of (Λ; τ∆+) has been studied.

Keywords

Hausdorff space, compactness, separability, supertightness.

Full Text:

PDF

References


A. V. Arhangelskii: Topological Function Spaces. Kluwer Academic Publishers, 1992.

L. Babinkostova, Lj. D. R. Kocinac ˇ and M. Scheepers: Combinatorics of open covers (VIII). Topol. Appl., 130 (1) (2003), 15–32.

A. Bella, M. Bonanzinga and M. V. Matveev: Variations of selective separability. Topol. Appl., 156 (2009), 1241–1252.

A. Bella and M. Sakai: Tight points of Pixley-Roy hyperspaces. Topol. Appl., 160 (2013), 2061–2068.

A. Caserta, G. Di Maio, Lj. D. R. Kocinac ˇ and E. Meccariello: Applications of k-covers II. Topol. Appl., 153 (2006), 3277–3293.

R. Cruz-Castillo, A. Ram´ırez-Paramo ´ and J. F. Tenorio: Menger and Mengertype star selection principles for hit-and-miss topology. Topol. Appl., 290, 107573, 2021.

G. Di Maio and L. Hol ´ a´: On hit-and-miss topologies. Rend. Accad. Sci. Fis. Mat. Napoli, 62 (1995), 103–124.

G. Di Maio and Lj. D. R. Kocinac ˇ : Some covering properties of hyperspaces. Topol. Appl., 155 (1718) (2008), 1959–1969.

G. Di Maio, Lj. D. R. Kocinac ˇ and E. Meccariello: Applications of k-covers. Acta Mathematica Sinica, English Series 22 (3) (2006), 1151–1160.

G. Di Maio, Lj. D. R. Kocinac ˇ and E. Meccariello: Selection principles and hyperspace topologies. Topol. Appl., 153 (56) (2005), 912–923.

J. Fell: A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff spaces. Proc. Amer. Math. Soc., 13 (1962), 372–376.

J. Gerlits and Zs. Nagy: Some properties of C(X), I. Topol. Appl., 13 (1982), 151–161.

I. Juhasz ´ and S. Shelah: l π(X) = δ(X) for compact X. Topol. Appl., 32 (3) (1989), 289–294.

W. Just, A. W. Miller, M. Scheepers and P. J. Szeptycki: The combinatorics of open covers, II. Topol. Appl., 73 (1996), 231–266.

Lj. D. R. Kocinac ˇ : Selected results on selection principles. in: Sh. Rezapour (Ed.), Proceedings of the 3rd Seminar on Geometry and Topology, July 15–17 (2003), Tabriz, Iran, 71–103.

Lj. D. R. Kocinac ˇ : γ-sets, γk-sets and hyperspaces. Math. Balkanica, 19 (2005), 109–118.

Lj. D. R. Kocinac ˇ and M. Scheepers: Combinatorics of open covers (VII): Groupability. Fundamenta Mathematicae, 179 (2) (2003), 131–155.

Lj. D. R. Kocinac ˇ and M. Scheepers: Function spaces and a property of Reznichenko. Topol. Appl., 123 (2002), 135–143.

Z. Li: Selection principles of the Fell topology and the Vietoris topology. Topol. Appl., 212 (2016), 90–104.

R.A. McCoy: Function spaces which are k-spaces. Topology Proc., 5 (1980), 139–136.

E. Michael: Topologies on spaces of subsets. Trans. Math. Soc., 71 (1951), 152–182.

M. Mrˇsevic´ and M. Jelic´: Selection principles in hyperspaces with generalized Vietoris topologies. Topol. Appl., 156 (1) (2008), 123–129.

H. Poppe: Eine Bemerkung u¨ber Trennungsaxiome in Raumen von abgeschlossenen Teilmengen topologisher Raume. Arch. Math., 16 (1965), 197–198.

M. Sakai: Cardinal functions of Pixley-Roy hypersaces. Topol. Appl., 159 (2012), 3080–3088.

M. Sakai: Property C” and function spaces. Proc. Amer. Math. Soc., 104 (3) (1988), 917–919.

M. Sakai: Selective separability of PixleyRoy hyperspaces. Topol. Appl., 159 (2012), 1591–1598.

M. Scheepers: Combinatorics of open covers I: Ramsey theory. Topol. Appl., 69 (1996), 31–62.

R. Sen: On some convergence properties of hyperspaces with hit-and-miss topology. Facta Universitatis, 37 (5) (2022), 1021–1035.

R. Sen and A. Ram´ırez-Paramo ´ : On c∆(Λ)-covers and ∆γ-sets. Topol. Appl., 307, 107930, 2022.

J. van Mill and C. F. Mills: On the character of supercompact spaces. Topology Proceedings, 3 (1978), 227–236.

L. Vietoris: Bereiche Zweiter Ordnung. Monatshefte Math. Phys., 33 (1923), 49–62.

L. Zsilinszky: Baire spaces and hyperspace topologies. Proc. Am. Math. Soc. 124 (1996), 3175–3184.




DOI: https://doi.org/10.22190/FUMI230329017S

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)