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## Fundamenta Mathematicae

1998 | 158 | 3 | 289-299
Tytuł artykułu

### Ordered spaces with special bases

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the roles played by four special types of bases (weakly uniform bases, ω-in-ω bases, open-in-finite bases, and sharp bases) in the classes of linearly ordered and generalized ordered spaces. For example, we show that a generalized ordered space has a weakly uniform base if and only if it is quasi-developable and has a $G_δ$-diagonal, that a linearly ordered space has a point-countable base if and only if it is first-countable and has an ω-in-ω base, and that metrizability in a generalized ordered space is equivalent to the existence of an OIF base and to the existence of a sharp base. We give examples showing that these are the best possible results.
Słowa kluczowe
EN
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
289-299
Opis fizyczny
Daty
wydano
1998
otrzymano
1998-02-02
poprawiono
1998-04-02
poprawiono
1998-06-01
Twórcy
autor
• We study the roles played by four special types of bases (weakly uniform bases, ω-in-ω bases, open-in-finite bases, and sharp bases) in the classes of linearly ordered and generalized ordered spaces. For example, we show that a generalized ordered space has a weakly uniform base if and only if it is quasi-developable and has a $G_δ$-diagonal, that a linearly ordered space has a point-countable base if and only if it is first-countable and has an ω-in-ω base, and that metrizability in a generalized ordered space is equivalent to the existence of an OIF base and to the existence of a sharp base. We give examples showing that these are the best possible results.
autor
• College of William and Mary, Williamsburg, Virginia 23187, U.S.A.
Bibliografia
• [AJRS] A. Arkhangel'skiĭ, W. Just, E. Reznichenko and P. Szeptycki, Sharp bases and weakly uniform bases versus point countable bases, Topology Appl., to appear.
• [BR] Z. Balogh and M. E. Rudin, Monotone normality, ibid. 47 (1992), 115-127.
• [B] H. Bennett, On quasi-developable spaces, Gen. Topology Appl. 1 (1971), 253-262.
• [B2] H. Bennett, Point-countability in linearly ordered spaces, Proc. Amer. Math. Soc. 28 (1971), 598-606.
• [BLP] H. Bennett, D. Lutzer, and S. Purisch, On dense subspaces of generalized ordered spaces, Topology Appl., to appear.
• [EL] R. Engelking and D. Lutzer, Paracompactness in ordered spaces, Fund. Math. 94 (1976), 49-58.
• [G] G. Gruenhage, A note on the point-countable base question, Topology Appl. 44 (1992), 157-162.
• [HL] R. Heath and W. Lindgren, Weakly uniform bases, Houston J. Math. 2 (1976), 85-90.
• [L] D. Lutzer. On generalized ordered spaces, Dissertationes Math. 89 (1971).
Typ dokumentu
Bibliografia
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