A space X is absolutely strongly star-Hurewicz if for each sequence (Un :n ∈ℕ/ of open covers of X and each dense subset D of X, there exists a sequence (Fn :n ∈ℕ/ of finite subsets of D such that for each x ∈X, x ∈St(Fn; Un) for all but finitely many n. In this paper, we investigate the relationships between absolutely strongly star-Hurewicz spaces and related spaces, and also study topological properties of absolutely strongly star-Hurewicz spaces.
@article{bwmeta1.element.doi-10_1515_math-2015-0004,
author = {Yan-Kui Song},
title = {Absolutely strongly star-Hurewicz spaces},
journal = {Open Mathematics},
volume = {13},
year = {2015},
zbl = {1322.54012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0004}
}
Yan-Kui Song. Absolutely strongly star-Hurewicz spaces. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0004/
[1] Bonanzinga M., Preservation and reflection of properties acc and hacc, Comment. Math. Univ. Carolinae., 1996, 37(1), 147-153 | Zbl 0917.54027
[2] Bonanzinga M., Cammaroto F., Kočinac Lj.D.R., Star-Hurewicz and related spaces, Applied General Topology., 2004, 5, 79-89 | Zbl 1080.54009
[3] Bonanzinga M., Cammaroto F., Kočinac Lj.D.R., Matveev M.V., On weaker forms of Menger, Rothberger and Hurewicz properties, Mat. Vesnik., 2009, 61, 13-23[WoS] | Zbl 1199.54139
[4] Bonanzinga M., Matveev M.V., Some covering properties for ψ-spaces, Mat. Vesnik., 2009, 61, 3-11 | Zbl 1199.54140
[5] Caserta A., Maio G. Di., Kočinac Lj.D.R., Versions of properties (a) and (pp), Topology Appl., 2011, 158, 1630-1638[WoS] | Zbl 1229.54029
[6] van Douwen E.K., Reed G.K., Roscoe A.W., Tree I.J., Star covering properties, Topology Appl., 1991, 39, 71-103[WoS] | Zbl 0743.54007
[7] van Douwen E.K., The integers and topology, in: Handbook of Set-theoretic Topology, Ed: K. Kunen and J. E. Vaughan, North- Holland, Amsterdam, 1984, 111-167
[8] Engelking E., General Topology, Revised and completed edition, Heldermann Verlag, Berlin, 1989,
[9] Fleischman W.M., A new extension of countable compactness, Fund. Math., 1971, 67, 1-7 | Zbl 0194.54601
[10] Gillman L., Jerison M., Rings of Continuous Functions, Van Nostrand, New York, 1960 | Zbl 0093.30001
[11] Kočinac Lj.D.R., Star-Menger and related spaces, Publ. Math. Debrecen., 1999, 55, 421-431 | Zbl 0932.54022
[12] Kočinac Lj.D.R., Star-Menger and related spaces II, Filomat (Ni˘s)., 1999, 13, 129-140
[13] Matveev M.V., A survey on star-covering properties, Topology Atlas, preprint No 330, 1998
[14] Matveev M.V., Absolutely countably compact spaces, Topology Appl., 1994, 59, 61-92 | Zbl 0801.54021
[15] Song Y.-K., On countable star-covering properties, Applied General Topology., 2007, 8(2), 249-258 | Zbl 1144.54312
[16] Song Y.-K., Absolutely strongly star-Menger spaces, Toplogy Appl., 2013, 160, 475-481 | Zbl 1270.54029
[17] Shi .W-X., Song Y.-K., Gao Y.-Z., Spaces embeddable as regular closed subsets into acc spaces and (a)-spaces, Topology Appl., 2005, 150, 19-31 | Zbl 1068.54020
[18] Vaughan J.E., Absolutely countably compactness and property (a), Talk at 1996 Praha Symposium on General Topology