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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 54 Issue: 1

The convexity induced by quasi-consistency and quasi-adjacency

Yongchao Wang(Beijing Institute of Technology)
Fu-gui Shı(Beijing Institute of Technology)0000-0001-8090-3872
Pages
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Publication Date
2025-02-28
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AI Summary & Key Takeaways

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

And we deeply study the relationships among these structures.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce (quasi-)consistent spaces and (quasi-)adjacent spaces to characterize convexity spaces.
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Key Findings & Data:Firstly, we show that convexity spaces can be characterized by quasi-consistent spaces.
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Conclusion & Impact:And we deeply study the relationships among these structures.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:convexity · remotehood system · quasi-consistency

Abstract

In this paper, we introduce (quasi-)consistent spaces and (quasi-)adjacent spaces to characterize convexity spaces. Firstly, we show that convexity spaces can be characterized by quasi-consistent spaces. They can be induced by each other. In particular, each convexity space can be quasi-consistentizable. Every quasi-consistency $\mathcal{U}$ can induce two hull operators and thus determine different convexities $\mathcal{C}^{\mathcal{U}}$ and $\mathcal{C}_{\mathcal{U}}$. And $\mathcal{C}^{\mathcal{U}}=\mathcal{C}_{\mathcal{U}}$ holds when $\mathcal{U}$ is a consistency. Secondly, we use quasi-adjacent spaces to characterize convexity spaces. Each convexity space can be quasi-adjacentizable. In both of characterizations of convexity, remotehood systems play an important role in inducing convexity. Finally, we show there exists a close relation between a quasi-consistency and a quasi-adjacency. Furthermore, there exists a one-to-one correspondence between a quasi-adjacency and a fully ordered quasi-consistency. And we deeply study the relationships among these structures.

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Cite This Article

Wang, Y., Shı, F. (2025). The convexity induced by quasi-consistency and quasi-adjacency. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 1. https://doi.org/10.15672/hujms.1320859

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