拓扑预序空间的拟伪度量化
Quasi-pseudo-metrization of topological preordered spaces
摘要：
我们证明了每隔一个可数完全正则预序空间（E，T，\leq）是拟伪度量空间，即在E上存在一个拟伪度量p，使得伪度量p \veep^- 1诱导T，并且\leq的图恰是集合{（x，y）：p（x，y）=0}.在有序的情况下，它被证明，这些空间可以被刻画为是序Hilbert立方体的子空间的顺序同胚。与双拓扑学中得到的准伪度量化结果的连接被澄清。特别地，严格拟伪度量化的有序空间被刻画为与有序希尔伯特立方体的有序子空间序同胚。
英文摘要：
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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