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Journals / Maltepe Journal of Mathematics / 2023 / Volume: 5 Issue: 2

About sequentially open and closed subsets in product spaces

Osman Mucuk(Erciyes University)0000-0001-7411-2871
Mina Betül Teke(ERCIYES UNIVERSITY)0009-0000-1168-7686
Pages
—
Publication Date
2023-11-30
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AI Summary & Key Takeaways

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

We will take the product spaces into account and give some results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We remind two facts for topological spaces.
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Key Findings & Data:The one is that in a Hausdorff space $X$ each sequence has a unique limit.
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Conclusion & Impact:We will take the product spaces into account and give some results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Sequentially convegence · product spaces · sequentially closed subset

Abstract

We remind two facts for topological spaces. The one is that in a Hausdorff space $X$ each sequence has a unique limit. This allows us to have a function from the set of all sequences in $X$ to $X$. Another is that in the first countable spaces some topological objects such as open subsets, closed subsets, closures and interiors of the sets, continuous functions and many others can be defined in terms of convergent sequences. In this paper we compare these notions with their sequential versions in topological spaces. We will take the product spaces into account and give some results.

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Cite This Article

Mucuk, O., Teke, M. B. (2023). About sequentially open and closed subsets in product spaces. Maltepe Journal of Mathematics, Volume: 5 Issue: 2. https://doi.org/10.47087/mjm.1301293

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