Left K-Cauchy regular maps between quasi-metric spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908565649752064 |
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| author | Singh, Om Dev Jindal, Anubha |
| author_facet | Singh, Om Dev Jindal, Anubha |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24619 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Left K-Cauchy regular maps between quasi-metric spaces Singh, Om Dev Jindal, Anubha General Topology Primary 54E40, Secondary 26A15, 30L99, 54E55, 54E99 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. |
| title | Left K-Cauchy regular maps between quasi-metric spaces |
| topic | General Topology Primary 54E40, Secondary 26A15, 30L99, 54E55, 54E99 |
| url | https://arxiv.org/abs/2509.24619 |