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JOURNALS // Ural Mathematical Journal // Archive

Ural Math. J., 2023 Volume 9, Issue 2, Pages 28–35 (Mi umj201)

This article is cited in 2 papers

Countable compactness modulo an ideal of natural numbers

Prasenjit Bal, Debjani Rakshit, Susmita Sarkar

ICFAI University Tripura

Abstract: In this article, we introduce the idea of $I$-compactness as a covering property through ideals of $\mathbb N$ and regardless of the $I$-convergent sequences of points. The frameworks of $s$-compactness, compactness and sequential compactness are compared to the structure of $I$-compact space. We began our research by looking at some fundamental characteristics, such as the nature of a subspace of an $I$-compact space, then investigated its attributes in regular and separable space. Finally, various features resembling finite intersection property have been investigated, and a connection between $I$-compactness and sequential $I$-compactness has been established.

Keywords: ideal, open cover, compact space, $I$-convergence.

Language: English

DOI: 10.15826/umj.2023.2.002



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© Steklov Math. Inst. of RAS, 2024