Left K-Cauchy regular maps between quasi-metric spaces

2025/09/29 by Om Dev Singh, Singh, Om Dev, Anubha Jindal +1 · 1 citation
Mathematics · #30L99 #54E55 #54E99 #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN) #Primary 54E40 #Secondary 26A15

paper · pdf · doi:10.48550/arxiv.2509.24619

openalex publication_date 2025/09/29 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

This article presents a systematic study of a class of maps between quasi-metric spaces that preserve left K-Cauchy sequences. We call such maps left K-Cauchy regular maps. Several characterizations of these maps have been given in terms of the structural properties of the underlying quasi-metric spaces. In particular, we characterize left K-Cauchy regular maps in terms of hereditarily precompact sets by using a suitable version of the classical Efremovic Lemma in the setting of quasi-metric spaces. In addition, we examine the relationship of left K-Cauchy regular maps with (forward) uniformly continuous and continuous maps and prove extension theorems for such maps.

Cited by

• Quasi-metric spaces on which real-valued continuous functions are uniformly continuous

Related

• On certain notions of precompactness, continuity and Lipschitz functions
• Ekeland, Takahashi and Caristi principles in preordered quasi-metric spaces
• On sequences in 2-normed spaces
• The theory of quasiregular mappings in metric spaces: progress and challenges
• Quasi-uniform type spaces