8 research outputs found
Quasi-pseudo-metrization of topological preordered spaces
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.Comment: Latex2e, 20 pages. v2: minor changes in the proof of theorem 2.