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Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 5

Quantale-valued uniform convergence towers for quantale-valued metric spaces

Gunther Jäger
Pages
1443–1453
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

For special choices of the quantale, the results specialize to metric spaces and probabilistic metric spaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We show that quantale-valued metric spaces and quantale-valued partial metric spaces allow natural quantale-valued uniform convergence structures.
📊
Key Findings & Data:We furthermore characterize quantale-valued metric spaces and quantale-valued partial metric spaces by these quantale-valued uniform convergence structures.
💡
Conclusion & Impact:For special choices of the quantale, the results specialize to metric spaces and probabilistic metric spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$L$-metric space · $L$-partial metric space · $L$-uniform convergence tower space

Abstract

We show that quantale-valued metric spaces and quantale-valued partial metric spaces allow natural quantale-valued uniform convergence structures. We furthermore characterize quantale-valued metric spaces and quantale-valued partial metric spaces by these quantale-valued uniform convergence structures. For special choices of the quantale, the results specialize to metric spaces and probabilistic metric spaces.

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Cite This Article

Jäger, G. (2022). Quantale-valued uniform convergence towers for quantale-valued metric spaces. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 5, 1443–1453. https://ajindex.com/articles/529793

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