- Tytuł:
- Ordered spaces with special bases
- Autorzy:
-
Bennett, Harold
Lutzer, David - Powiązania:
- https://bibliotekanauki.pl/articles/1205288.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
point-countable base
weakly uniform base
ω-in-ω base
open-in-finite base
sharp base
metrizable space
quasi-developable space
linearly ordered space
generalized ordered space - Opis:
- 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.
- Źródło:
-
Fundamenta Mathematicae; 1998, 158, 3; 289-299
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł