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arXiv · 1202.4648

Quasi-pseudo-metrization of topological preordered spaces

E. Minguzzi
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Abstract

We establish that every second countable completely regularly preordered space (E,T,\leq) is quasi-pseudo-metrizable, in the sense that there is a quasi-pseudo-metric p on E for which the pseudo-metric p\veep^-1 induces T and the graph of \leq is exactly the set {(x,y): p(x,y)=0}. 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-pseudometrizable ordered spaces are characterized as being order homeomorphic to order subspaces of the ordered Hilbert cube.

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E. Minguzzi. 2012-02-21. Quasi-pseudo-metrization of topological preordered spaces. https://doi.org/10.1016/j.topol.2012.05.029

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