Abstract

We study certain diagonal axioms defined for quantale-valued Cauchy tower spaces and their relations to similar diagonal axioms for quantale-valued convergence tower spaces and quantale-valued uniform limit tower spaces. We construct a completion for a quantale-valued Cauchy tower space that preserves a diagonal axiom and show that our construction is the coarsest possible such completion.

Keywords: Cauchy space; quantale-valued Cauchy tower space; quantale-valued metric space; quantale-valued convergence tower space; diagonal axioms; completeness; completion.

MSC: 54E15, 54A20, 54A40, 54D35

DOI: 10.57016/MV-RQ818zz5

Pages:  263--276     

Volume  77 ,  Issue  3 ,  2025