A study on quasi-pseudometrics

Authors : Natasha DEMETRİOU, Hanspeter A KÜNZİ

Pages : 33-52

View : 25 | Download : 10

Publication Date : 2017-02-01

Article Type : Research Paper

Abstract :We study some aspects of the space $QPMinsert ignore into journalissuearticles values(X);$ of all quasi-pseudometrics on a set $X$ equipped with the extended $T_0$-quasi-metric $A_Xinsert ignore into journalissuearticles values(f,g);=\sup_{insert ignore into journalissuearticles values(x,y);\in X\times X}insert ignore into journalissuearticles values(finsert ignore into journalissuearticles values(x,y);-ginsert ignore into journalissuearticles values(x,y););$ whenever $f,g\in QPMinsert ignore into journalissuearticles values(X);$. We observe that this space is bicomplete and exhibit various closed subspaces of $insert ignore into journalissuearticles values( QPMinsert ignore into journalissuearticles values(X);, \tauinsert ignore into journalissuearticles values(insert ignore into journalissuearticles values(A_X);^s););$. 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 $insert ignore into journalissuearticles values(A_X);^sinsert ignore into journalissuearticles values(f,f^{-1});.
Keywords : quasi pseudometric, T 0 quasi metric, nonnegatively weightable quasi pseudometric