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Journals / Turkish Journal of Mathematics / 2006 / Cilt: 30 - Sayı: 3

Connectedness in Isotonic Spaces

Eissa D. HABIL
Khalid A. ELZENATI
Pages
247–262
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

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

We further extend the notions of Z-connectedness and strong connectedness to isotonic spaces, and we indicate the intimate relationship between these notions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:An isotonic space (X,cl) is a set X with isotonic operator cl:P(X) \to P(X) which satisfies cl(\emptyset) = \emptyset and cl(A)\subseteq cl(B) whenever A\subseteq B\subseteq X.
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Key Findings & Data:Many properties which hold in topological spaces hold in isotonic spaces as well.
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Conclusion & Impact:We further extend the notions of Z-connectedness and strong connectedness to isotonic spaces, and we indicate the intimate relationship between these notions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:generalized closure spaces · isotonic spaces · neighborhood spaces

Abstract

An isotonic space (X,cl) is a set X with isotonic operator cl:P(X) \to P(X) which satisfies cl(\emptyset) = \emptyset and cl(A)\subseteq cl(B) whenever A\subseteq B\subseteq X. Many properties which hold in topological spaces hold in isotonic spaces as well. The notion of connectedness that is familiar from topological spaces generalizes to isotonic spaces. We further extend the notions of Z-connectedness and strong connectedness to isotonic spaces, and we indicate the intimate relationship between these notions.

Özet

An isotonic space (X,cl) is a set X with isotonic operator cl:P(X) \to P(X) which satisfies cl(\emptyset) = \emptyset and cl(A)\subseteq cl(B) whenever A\subseteq B\subseteq X. Many properties which hold in topological spaces hold in isotonic spaces as well. The notion of connectedness that is familiar from topological spaces generalizes to isotonic spaces. We further extend the notions of Z-connectedness and strong connectedness to isotonic spaces, and we indicate the intimate relationship between these notions.

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Cite This Article

HABIL, E. D., ELZENATI, K. A. (2022). Connectedness in Isotonic Spaces. Turkish Journal of Mathematics, Cilt: 30 - Sayı: 3, 247–262. https://ajindex.com/articles/608688

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  16. Eissa D. HABIL, Khalid A. ELZENATI Department of Mathematics Islamic University of Gaza P. O. Box 108 Gaza, Palestine e-mail: [email protected] e-mail: [email protected]