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Ordered spaces with special bases

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Bennett H. R., Lutzer D. J.

Fundamenta Mathematicae

1998

tom 158

nr 3

289-299

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Bennett H. R.

1 Lutzer D. J.

1 1998

Wyniki wyszukiwania

Ordered spaces with special bases