On I^K-Convergence in a Topological space via semi-open sets

2021/03/27 by Ankur Sharmah, Sharmah, Ankur, Debajit Hazarika +1
Decision Sciences · Mathematics · #40A35 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Primary: 54A20 #Rings, Modules, and Algebras #Secondary: 40A05

paper · pdf · doi:10.48550/arxiv.2103.14841

openalex publication_date 2021/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we consider I^K-convergence to define a new concept of convergence namely, S-I^K-convergence which generalizes the notion of S-I-convergence introduced by Guevara et al. \citeGSR20 recently. Some properties of S-I^K-convergence of sequences and its relation with compact sets are discussed. In particular, we investigate the relation between semi-compactness and semi-Lindeloffness by introducing the notion of S-I^K-cluster point of a sequence. The "Equivalence between semi-dense and dense sets" is utilized to characterize the set of S-I^K-cluster points of a sequence as semi-closed subsets of a topological space. Moreover, in product space, we obtain some results for I^K-convergence which also holds for S-I^K-convergence.

Related

• Further aspects of I^K-convergence in Topological Spaces
• \mathcal I^K-limit points, \mathcal I^K-cluster points and \mathcal I^K-Frechet compactness
• A Note on I^K and I^K*-convergence in topological spaces
• Characterizations of Ideal Cluster Points
• I and I*-soft convergence in soft topological spaces