Quasi-pseudo-metrization of topological preordered spaces

Details Quasi-pseudo-metrization of topological preordered spaces Quasi-pseudo-metrization of topological preordered spaces

2012-02-21

arxiv.org/abs/1202.4648v1

Mathematics

General Topology

20 pages

Scientific paper

We establish that every second countable completely regularly preordered space is quasi-pseudo-metrizable. In the ordered case it is proved that these spaces can be characterized as being order homeomorphic to subspaces of the ordered Hilbert cube. The connection with quasi-pseudo-metrization results obtained in bitopology is clarified. In particular, strictly quasi-pseudo-metrizable ordered spaces are characterized as being order homeomorphic to order subspaces of the ordered Hilbert cube.

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