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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 4

The relationship between pointwise $k$-pseudo metrics and pointwise $k$-closed ball systems

Yu Zhong(North China University of Technology)0009-0008-8333-3519
Jiayi Zeng(North China University of Technology)0009-0001-2558-2524
Zhi-Hui Yang(North China University of Technology)0009-0003-9734-188X
Pages
—
Publication Date
2026-08-17
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, some $L$-structures induced by a pointwise $k$-closed ball system are obtained, including an $L$-neighborhood system, an $L$-interior operator and an $L$-topology ($L$ denotes a completely distributive De Morgan algebra).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce a definition of a pointwise $k$-pseudo metric which is a generalization of pointwise pseudo metric.
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Key Findings & Data:Then we discuss the axiomatic characterizations of a pointwise $k$-pseudo metric by a pointwise $k$-closed ball system that can be regarded as the opposite of the corresponding pointwise $k$-open ball system.
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Conclusion & Impact:Finally, some $L$-structures induced by a pointwise $k$-closed ball system are obtained, including an $L$-neighborhood system, an $L$-interior operator and an $L$-topology ($L$ denotes a completely distributive De Morgan algebra).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:pointwise k-pseudo metric · pointwise k-closed ball system · L-neighborhood system

Abstract

In this paper, we introduce a definition of a pointwise $k$-pseudo metric which is a generalization of pointwise pseudo metric. Then we discuss the axiomatic characterizations of a pointwise $k$-pseudo metric by a pointwise $k$-closed ball system that can be regarded as the opposite of the corresponding pointwise $k$-open ball system. Moreover, it is proved that there is a one-to-one correspondence between pointwise $k$-pseudo metrics and symmetric pointwise $k$-closed ball systems, and the symmetry conditions are different and simpler than the previous symmetry conditions. Finally, some $L$-structures induced by a pointwise $k$-closed ball system are obtained, including an $L$-neighborhood system, an $L$-interior operator and an $L$-topology ($L$ denotes a completely distributive De Morgan algebra).

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Cite This Article

Zhong, Y., Zeng, J., Yang, Z. (2026). The relationship between pointwise $k$-pseudo metrics and pointwise $k$-closed ball systems. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 4. https://doi.org/10.15672/hujms.1838784

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