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Ordered Cauchy spaces.

Kent, Darrell C., Vainio, R. (1985)

International Journal of Mathematics and Mathematical Sciences

Ordered spaces and quasi-uniformities on spaces of continuous order-preserving functions.

Koena Rufus Nailana (2000)

Extracta Mathematicae

In this paper we introduce and investigate the notions of point open order topology, compact open order topology, the order topology of quasi-uniform pointwise convergence and the order topology of quasi-uniform convergence on compacta. We consider the functorial correspondence between function spaces in the categories of topological spaces, bitopological spaces and ordered topological spaces. We obtain extensions to the topological ordered case of classical topological results on function spaces....

Ordered spaces with special bases

Harold Bennett, David Lutzer (1998)

Fundamenta Mathematicae

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...

Order-like structure of monotonically normal spaces

Scott W. Williams, Hao Xuan Zhou (1998)

Commentationes Mathematicae Universitatis Carolinae

For a compact monotonically normal space X we prove:   (1)   X has a dense set of points with a well-ordered neighborhood base (and so X is co-absolute with a compact orderable space);   (2)   each point of X has a well-ordered neighborhood π -base (answering a question of Arhangel’skii);   (3)   X is hereditarily paracompact iff X has countable tightness. In the process we introduce weak-tightness, a notion key to the results above and yielding some cardinal function results on monotonically normal...

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