On a generalization of quasi-metric space
Abstract
We introduce a distinctive metric structure for generalized topology by extending the quasi-metric. This extension (to be called gquasi metric) naturally induces a generalized topology, yet it may diverge from forming a topology. We demonstrate that g-quasi metrizability remains an invariant property of generalized topological spaces. Expanding the concepts of metric product and uniform continuity within g-quasi metric spaces, we observe an instance where a g-quasi metric may not exhibit uniform continuity like standard metrics. Additionally, we study completeness, Lebesgue property, and weak G-completeness for g-quasi metric spaces.
Fields of Study & Subjects
Fixed Point Theorems Analysis
Fuzzy and Soft Set Theory
Advanced Topology and Set Theory
Publication details
- Journal / source
- Acta et Commentationes Universitatis Tartuensis de Mathematica
- Volume
- 30
- Issue
- 1
- Pages
- 5–17
- Publication date
- 30 May 2026
- Language
- EN