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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 53 Issue: 2

The Vietoris hyperspace $\mathcal F(X)$ and certain generalized metric properties

Luong Quoc Tuyen(Da Nang University of Education)0000-0002-4330-0746
Tuyen Ong Van(Hoa Vang High School)0000-0002-0232-2092
Ljubiša D. R. Kočinac(University of Nis)0000-0002-4870-7908
Pages
—
Publication Date
2024-04-23
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AI Summary & Key Takeaways

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

Also, we obtain some results related to the images of metric spaces under some kinds of continuous mappings.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study several generalized metric properties of the space $\mathcal F(X)$ of finite subsets of a space $X$ endowed with the Vietoris topology.
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Key Findings & Data:In particular, we consider such properties $(P)$ for which $\mathcal F(X)$ has $(P)$ if and only if $X$ has $(P)$.
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Conclusion & Impact:Also, we obtain some results related to the images of metric spaces under some kinds of continuous mappings.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:hyperspace · generalized metric properties · $cs$-cover

Abstract

In this paper, we study several generalized metric properties of the space $\mathcal F(X)$ of finite subsets of a space $X$ endowed with the Vietoris topology. In particular, we consider such properties $(P)$ for which $\mathcal F(X)$ has $(P)$ if and only if $X$ has $(P)$. Also, we obtain some results related to the images of metric spaces under some kinds of continuous mappings.

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Cite This Article

Tuyen, L. Q., Van, T. O., Kočinac, L. D. R. (2024). The Vietoris hyperspace $\mathcal F(X)$ and certain generalized metric properties. Hacettepe Journal of Mathematics and Statistics, Volume: 53 Issue: 2. https://doi.org/10.15672/hujms.1203236

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