Absolutely strongly star-Hurewicz spaces

Yan-Kui Song

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page 26-32, electronic only
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Yan-Kui Song. "Absolutely strongly star-Hurewicz spaces." Open Mathematics 13.1 (2015): 26-32, electronic only. <http://eudml.org/doc/268823>.

@article{Yan2015,
abstract = {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.},
author = {Yan-Kui Song},
journal = {Open Mathematics},
keywords = {Selection principles; Starcompact; acc; Strongly star-Menger; Absolutely strongly star-Menger; Strongly star-Hurewicz; Absolutely strongly star-Hurewicz; Alexandroff duplicate; countably compact; starcompact; strongly star-Menger; absolutely strongly star-Menger; strongly star-Hurewicz; absolutely strongly star-Hurewicz},
language = {eng},
number = {1},
pages = {26-32, electronic only},
title = {Absolutely strongly star-Hurewicz spaces},
url = {http://eudml.org/doc/268823},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Yan-Kui Song
TI - Absolutely strongly star-Hurewicz spaces
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 26
EP - 32, electronic only
AB - 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.
LA - eng
KW - Selection principles; Starcompact; acc; Strongly star-Menger; Absolutely strongly star-Menger; Strongly star-Hurewicz; Absolutely strongly star-Hurewicz; Alexandroff duplicate; countably compact; starcompact; strongly star-Menger; absolutely strongly star-Menger; strongly star-Hurewicz; absolutely strongly star-Hurewicz
UR - http://eudml.org/doc/268823
ER -

References

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  1. [1] Bonanzinga M., Preservation and reflection of properties acc and hacc, Comment. Math. Univ. Carolinae., 1996, 37(1), 147-153 Zbl0917.54027
  2. [2] Bonanzinga M., Cammaroto F., Kočinac Lj.D.R., Star-Hurewicz and related spaces, Applied General Topology., 2004, 5, 79-89 Zbl1080.54009
  3. [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] Zbl1199.54139
  4. [4] Bonanzinga M., Matveev M.V., Some covering properties for ψ-spaces, Mat. Vesnik., 2009, 61, 3-11 Zbl1199.54140
  5. [5] Caserta A., Maio G. Di., Kočinac Lj.D.R., Versions of properties (a) and (pp), Topology Appl., 2011, 158, 1630-1638[WoS] Zbl1229.54029
  6. [6] van Douwen E.K., Reed G.K., Roscoe A.W., Tree I.J., Star covering properties, Topology Appl., 1991, 39, 71-103[WoS] Zbl0743.54007
  7. [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. [8] Engelking E., General Topology, Revised and completed edition, Heldermann Verlag, Berlin, 1989, 
  9. [9] Fleischman W.M., A new extension of countable compactness, Fund. Math., 1971, 67, 1-7 Zbl0194.54601
  10. [10] Gillman L., Jerison M., Rings of Continuous Functions, Van Nostrand, New York, 1960 Zbl0093.30001
  11. [11] Kočinac Lj.D.R., Star-Menger and related spaces, Publ. Math. Debrecen., 1999, 55, 421-431 Zbl0932.54022
  12. [12] Kočinac Lj.D.R., Star-Menger and related spaces II, Filomat (Ni˘s)., 1999, 13, 129-140 
  13. [13] Matveev M.V., A survey on star-covering properties, Topology Atlas, preprint No 330, 1998 
  14. [14] Matveev M.V., Absolutely countably compact spaces, Topology Appl., 1994, 59, 61-92 Zbl0801.54021
  15. [15] Song Y.-K., On countable star-covering properties, Applied General Topology., 2007, 8(2), 249-258 Zbl1144.54312
  16. [16] Song Y.-K., Absolutely strongly star-Menger spaces, Toplogy Appl., 2013, 160, 475-481 Zbl1270.54029
  17. [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 Zbl1068.54020
  18. [18] Vaughan J.E., Absolutely countably compactness and property (a), Talk at 1996 Praha Symposium on General Topology 

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