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Journals / Journal of Universal Mathematics / 2026 / Cilt: 6 Sayı: 1

THEORY OF GENERALIZED CONNECTEDNESS (g-Tg-CONNECTEDNESS) IN GENERALIZED TOPOLOGICAL SPACES (Tg-SPACES)

Mohammad Irshad Khodabocus(University of Mauritius)0000-0003-2252-4342
Noor-ul-hacq Sookıa(University of Mauritius)0000-0002-3155-0473
Pages
1–38
Publication Date
2023-01-31
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AI Summary & Key Takeaways

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

Diagrams establish the various relationships amongst these types of g-Tg-connectedness presented here and in the literature, and a nice application supports the overall theory.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the definitions of novel classes of generalized connected sets (briefly, g-Tg-connected sets) and generalized disconnected sets (briefly, g-Tg-disconnected sets) in generalized topological spaces (briefly, Tg-spaces) are defined in terms of generalized sets (briefly, g-Tg -sets) and, their properties and characterizations with respect to set-theoretic relations are presented.
📊
Key Findings & Data:The basic properties and characterizations of the notions of local, pathwise, local pathwise and simple g-Tg-connectedness are also presented.
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Conclusion & Impact:Diagrams establish the various relationships amongst these types of g-Tg-connectedness presented here and in the literature, and a nice application supports the overall theory.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Generalized topological space (Tg-spaces) · generalized local connectedness (local g-Tg-connectedness) · generalized pathwise connectedness (pathwise g-Tg-connectedness)

Abstract

In this paper, the definitions of novel classes of generalized connected sets (briefly, g-Tg-connected sets) and generalized disconnected sets (briefly, g-Tg-disconnected sets) in generalized topological spaces (briefly, Tg-spaces) are defined in terms of generalized sets (briefly, g-Tg -sets) and, their properties and characterizations with respect to set-theoretic relations are presented. The basic properties and characterizations of the notions of local, pathwise, local pathwise and simple g-Tg-connectedness are also presented. The study shows that local pathwise g-Tg -connectedness implies local g-Tg-connectedness, pathwise g-Tg-connectedness implies g-Tg-connectedness, and g-Tg-connectedness is a Tg-property. Diagrams establish the various relationships amongst these types of g-Tg-connectedness presented here and in the literature, and a nice application supports the overall theory.

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Cite This Article

Khodabocus, M. I., Sookıa, N. (2023). THEORY OF GENERALIZED CONNECTEDNESS (g-Tg-CONNECTEDNESS) IN GENERALIZED TOPOLOGICAL SPACES (Tg-SPACES). Journal of Universal Mathematics, Cilt: 6 Sayı: 1, 1–38. https://doi.org/10.33773/jum.1149387

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