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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2023 / Cilt: 72 Sayı: 1

New types of connectedness and intermediate value theorem in ideal topological spaces

Ferit YALAZ
Aynur KESKİN KAYMAKCI
Pages
259–285
Publication Date
2023-03-30
DOI
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AI Summary & Key Takeaways

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

Also, for some special cases, it is shown that the intermediate value theorem in ideal topological spaces and the intermediate value theorem in topological spaces coincide.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The definitions of new type separated subsets are given in ideal topological spaces.
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Key Findings & Data:By using these definitions, we introduce new types of connectedness.
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Conclusion & Impact:Also, for some special cases, it is shown that the intermediate value theorem in ideal topological spaces and the intermediate value theorem in topological spaces coincide.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ideal topological space · local function · local closure function

Abstract

The definitions of new type separated subsets are given in ideal topological spaces. By using these definitions, we introduce new types of connectedness. It is shown that these new types of connectedness are more general than some previously defined concepts of connectedness in ideal topological spaces. The new types of connectedness are compared with well-known connectedness in point-set topology. Then, the intermediate value theorem for ideal topological spaces is given. Also, for some special cases, it is shown that the intermediate value theorem in ideal topological spaces and the intermediate value theorem in topological spaces coincide.

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Cite This Article

YALAZ, F., KAYMAKCI, A. K. (2023). New types of connectedness and intermediate value theorem in ideal topological spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 72 Sayı: 1, 259–285. https://ajindex.com/articles/903590

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