Lebesgue Property and G-completeness in Generalized Quasi-uniform Spaces

2023/11/04 by Sugata Adhya, Adhya, Sugata, A. Deb Ray +1
Mathematics · Decision Sciences · #Fixed Point Theorems Analysis #Fuzzy and Soft Set Theory #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.2311.02325

Abstract

This paper extends the Lebesgue property and (weak) G-completeness to generalized quasi-uniform spaces. It investigates the connections between completeness, (weak) G-completeness, and the Lebesgue property of the product of generalized quasi-uniform spaces with those of the component spaces. It has been observed that the related behaviors differ for the Lebesgue property in contrast to completeness and (weak) G-completeness.

Related

• On Stoltenberg's quasi-uniform completion
• On a Generalization of Quasi-metric Space
• A solution to the completion problem of quasi-uniform spaces
• Quasi Grand Lebesgue Spaces
• The bicompletion of the Hausdorff quasi-uniformity