Gromov-Hausdorff compactness theorem for non-Archimedean Fuzzy Metric Spaces

TL;DR

This paper extends the Gromov-Hausdorff compactness theorem to non-Archimedean fuzzy metric spaces, providing a fuzzy precompactness theorem that generalizes classical results.

Contribution

It introduces a fuzzy version of Gromov's precompactness theorem for non-Archimedean fuzzy metric spaces, completing the theoretical framework for fuzzy Gromov-Hausdorff distances.

Findings

Established a fuzzy precompactness theorem for non-Archimedean fuzzy metric spaces.

Connected fuzzy Gromov-Hausdorff distances with classical metric space results.

Extended the previous fuzzy Gromov-Hausdorff completeness theorem.

Abstract

The authors introduced in a previous paper the notion of fuzzy Gromov-Hausdorff distance between non-Archimedean compact fuzzy metric spaces, presenting a fuzzy version of the Gromov's completeness theorem. In this paper we present a fuzzy version of the Gromov's precompactness theorem which allows to deduce the classical theorem for compact metric spaces by means of the standard fuzzy metric associated to a metric space. This completes the previous work.