A study on quasi-pseudometrics
Authors : Natasha Demetriou, Hans-peter A. Künzi
Pages : 33-52
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Publication Date : 2017-02-01
Article Type : Research
Abstract :We study some aspects of the space $QPM(X)$ of all quasi-pseudometrics on a set $X$ equipped with the extended $T_0$-quasi-metric $A_X(f,g)=\sup_{(x,y)\in X\times X}(f(x,y)-g(x,y))$ whenever $f,g\in QPM(X)$. We observe that this space is bicomplete and exhibit various closed subspaces of $( QPM(X), \tau((A_X)^s))$. In the second part of the paper, as a rough way to measure the asymmety of a quasi-pseudometric $f$ on a set $X$, we investigate some properties of the value $(A_X)^s(f,f^{-1}).Keywords : quasi-pseudometric, $T_0$-quasi-metric, nonnegatively weightable quasi-pseudometric