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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 5

Maps that preserve left (right) $K$-Cauchy sequences

Olivier Olela Otafudu
Pages
1466–1476
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Moreover, we characterize totally bounded sets on a quasi-pseudometric space in terms of maps that preserve left $K$-Cauchy and right $K$-Cauchy sequences and uniformly locally semi-Lipschitz maps.

📌 3 Key Takeaways

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Objective & Hypothesis:It is well-known that on quasi-pseudometric space $(X,q)$, every $q^s$-Cauchy sequence is left (or right) $K$-Cauchy sequence but the converse does not hold in general.
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Key Findings & Data:In this article, we study a class of maps that preserve left (right) $K$-Cauchy sequences that we call left (right) $K$-Cauchy sequentially-regular maps.
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Conclusion & Impact:Moreover, we characterize totally bounded sets on a quasi-pseudometric space in terms of maps that preserve left $K$-Cauchy and right $K$-Cauchy sequences and uniformly locally semi-Lipschitz maps.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cauchy sequential regularity · left $K$-Cauchy · bornology

Abstract

It is well-known that on quasi-pseudometric space $(X,q)$, every $q^s$-Cauchy sequence is left (or right) $K$-Cauchy sequence but the converse does not hold in general. In this article, we study a class of maps that preserve left (right) $K$-Cauchy sequences that we call left (right) $K$-Cauchy sequentially-regular maps. Moreover, we characterize totally bounded sets on a quasi-pseudometric space in terms of maps that preserve left $K$-Cauchy and right $K$-Cauchy sequences and uniformly locally semi-Lipschitz maps.

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Cite This Article

Otafudu, O. O. (2022). Maps that preserve left (right) $K$-Cauchy sequences. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 5, 1466–1476. https://ajindex.com/articles/529451

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