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Journals / Hacettepe Journal of Mathematics and Statistics / 2017 / Cilt: 46 - Sayı: 1

Functional equivalence of topological spaces and topological modules

Mitrofan M. CHOBAN
Radu N. Dumbr VEANU
Pages
77–90
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

Some conditions under which the topological property $\mathcal{P}$ is preserved by the $l_p(E,F)$-equivalence (Theorems 6.3, 6.4, 7.3 and 8.1) are given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let $R$ be a topological ring and $E$, $F$ be unitary topological $R$-modules.
📊
Key Findings & Data:Denote by $C_p(X,E)$ the class of all continuous mappings of $X$ into $E$ in the topology of pointwise convergence.
💡
Conclusion & Impact:Some conditions under which the topological property $\mathcal{P}$ is preserved by the $l_p(E,F)$-equivalence (Theorems 6.3, 6.4, 7.3 and 8.1) are given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Function space · topology of pointwise convergence · support

Abstract

Let $R$ be a topological ring and $E$, $F$ be unitary topological $R$-modules. Denote by $C_p(X,E)$ the class of all continuous mappings of $X$ into $E$ in the topology of pointwise convergence. The spaces $X$ and $Y$ are called $l_p(E,F)$-equivalent if the topological $R$-modules $C_p(X,E)$ and $C_p(Y,F)$ are topological isomorphic. Some conditions under which the topological property $\mathcal{P}$ is preserved by the $l_p(E,F)$-equivalence (Theorems 6.3, 6.4, 7.3 and 8.1) are given.

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Cite This Article

CHOBAN, M. M., VEANU, R. N. D. (2022). Functional equivalence of topological spaces and topological modules. Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 1, 77–90. https://ajindex.com/articles/529988

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