We establish that every second countable completely regularly preordered space (E,T,<) is quasi-pseudo-metrizable, in the sense that there is a quasi-pseudo-metric p on E for which the pseudo-metric p∨p^−1 induces T and the graph of < 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-pseudo-metrizable ordered spaces are characterized as being order homeomorphic to order subspaces of the ordered Hilbert cube.
Quasi-pseudo-metrization of topological preordered spaces / Minguzzi, Ettore. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - STAMPA. - 159:(2012), pp. 2888-2898. [10.1016/j.topol.2012.05.029]
Quasi-pseudo-metrization of topological preordered spaces
MINGUZZI, ETTORE
2012
Abstract
We establish that every second countable completely regularly preordered space (E,T,<) is quasi-pseudo-metrizable, in the sense that there is a quasi-pseudo-metric p on E for which the pseudo-metric p∨p^−1 induces T and the graph of < 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-pseudo-metrizable ordered spaces are characterized as being order homeomorphic to order subspaces of the ordered Hilbert cube.File | Dimensione | Formato | |
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Minguzzi - Quasi-pseudo-metrization of topological preordered spaces - Topol. Appl. 159 (2012) 2888-2898.pdf
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