Quantale-valued uniform convergence towers for quantale-valued metric spaces

Year 2019, Volume: 48 Issue: 5, 1443 - 1453, 08.10.2019

Gunther Jäger

Abstract

We show that quantale-valued metric spaces and quantale-valued partial metric spaces allow natural quantale-valued uniform convergence structures. We furthermore characterize quantale-valued metric spaces and quantale-valued partial metric spaces by these quantale-valued uniform convergence structures. For special choices of the quantale, the results specialize to metric spaces and probabilistic metric spaces.

Keywords

$L$-metric space , $L$-partial metric space , $L$-uniform convergence tower space

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