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2013 | 11 | 9 | 1635-1642
Tytuł artykułu

On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces

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Języki publikacji
EN
Abstrakty
EN
We introduce the concept of a family of sets generating another family. Then we prove that if X is a topological space and X has W = {W(x): x ∈ X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of ω-rank, then X is metaLindelöf as well as a countable product of them. We also prove that if W satisfies ω-rank (F) and, for every x ∈ X, W(x) is of the form W 0(x) ∪ W 1(x), where W 0(x) is Noetherian and W 1(x) consists of neighbourhoods of x, then X is metacompact.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
9
Strony
1635-1642
Opis fizyczny
Daty
wydano
2013-09-01
online
2013-06-28
Twórcy
autor
Bibliografia
  • [1] Collins P.J., Reed G.M., Roscoe A.W., Rudin M.E., A lattice of conditions on topological spaces, Proc. Amer. Math. Soc., 1985, 94(3), 487–496 http://dx.doi.org/10.1090/S0002-9939-1985-0787900-X
  • [2] Erdős P., Hajnal A., Máté A., Rado R., Combinatorial Set Theory: Partition Relations for Cardinals, Stud. Logic Found. Math., 106, North-Holland, Amsterdam-New York-Oxford, 1984
  • [3] Gartside P.M., Moody P.J., Well-ordered (F) spaces, Topology Proc., 1992, 17, 111–130
  • [4] Gruenhage G., Nyikos P., Spaces with bases of countable rank, General Topology and Appl., 1978, 8(3), 233–257 http://dx.doi.org/10.1016/0016-660X(78)90004-1
  • [5] Hajnal A., Hamburger P., Set Theory, London Math. Soc. Stud. Texts, 48, Cambridge University Press, Cambridge, 1999 http://dx.doi.org/10.1017/CBO9780511623561
  • [6] Moody P.J., Reed G.M., Roscoe A.W., Collins P.J., A lattice of conditions on topological spaces. II, Fund. Math., 1991, 138(2), 69–81
  • [7] Nagata J., On dimension and metrization, In: General Topology and its Relations to Modern Analysis and Algebra, Prague, 1961, Academic Press, New York, 1962, 282–285
  • [8] Nyikos P.J., Some surprising base properties in topology. II, In: Set-Theoretic Topology, Athens, 1975–1976, Academic Press, New York-London, 1977, 277–305
  • [9] Vural Ç., Some weaker forms of the chain (F) condition for metacompactness, J. Aust. Math. Soc., 2008, 84(2), 283–288 http://dx.doi.org/10.1017/S1446788708000037
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0271-3
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