On Weak $G$-Completeness for Fuzzy Metric Spaces

TL;DR

This paper characterizes weak G-completeness in fuzzy metric spaces, shows their completeness, and explores conditions for their fuzzy metric completions, also drawing parallels with classical metric spaces.

Contribution

It provides equivalent characterizations of weak G-complete fuzzy metric spaces and relates these to their completions, extending classical results.

Findings

Weak G-complete fuzzy metric spaces are complete.

Characterizations of spaces with weak G-complete fuzzy metric completions.

Analogous results established for classical metric spaces.

Abstract

In this paper, we provide equivalent characterizations of weak $G$-complete fuzzy metric spaces. Since such spaces are complete, we also characterize fuzzy metric spaces that have weak $G$-complete fuzzy metric completions. Moreover we establish analogous results for classical metric spaces.