COUNTABLE COMPACTNESS MODULO AN IDEAL OF NATURAL NUMBERS

Prasenjit Bal     (Department of Mathematics, ICFAI University Tripura, Kamalghat, 799210, India)
Debjani Rakshit     (Department of Mathematics, ICFAI University Tripura, Kamalghat, 799210, India)
Susmita Sarkar     (Department of Mathematics, ICFAI University Tripura, Kamalghat, 799210, India)

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.

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References


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DOI: http://dx.doi.org/10.15826/umj.2023.2.002

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