2021/06/30 by Manoranjan Singha, Singha, Manoranjan, Roy, Sima
Decision Sciences · Mathematics · #40A35 #54A20 #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.2107.00050
openalex publication_date 2021/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One of the main obstacle to study compactness in topological spaces via ideals was the definition of ideal convergence of subsequences as in the existing literature according to which subsequence of an ideal convergent sequence may fail to be ideal convergent with respect to same ideal. This obstacle has been get removed in this article and notions of I compactness as well as I star compactness of topological spaces have been introduced and studied to some extent. Involvement of I nonthin subsequences in the definition of I and I star compactness make them different from compactness even in metric spaces.