Further aspects of I^K-convergence in Topological Spaces

2020/12/23 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) #Iterative Methods for Nonlinear Equations #Primary: 54A20 #Secondary: 40A05

paper · pdf · doi:10.48550/arxiv.2012.12484

openalex publication_date 2020/12/23 · openalex created_date 2021/01/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain some results on the relationships between different ideal \linebreak convergence modes namely, I^K, I^{K^*}, I, K, I ∪ K and (I ∪ K)^*. We introduce a topological space namely I^K-sequential space and show that the class of I^K-sequential spaces contain the sequential spaces. Further I^K-notions of cluster points and limit points of a function are also introduced here. For a given sequence in a topological space X, we characterize the set of I^K-cluster points of the sequence as closed subsets of X.

Citations

• A Note on I^K and I^K*-convergence in topological spaces

Related

• On I^K-Convergence in a Topological space via semi-open sets
• \mathcal I^K-limit points, \mathcal I^K-cluster points and \mathcal I^K-Frechet compactness
• Some properties of I*-sequential topological space
• A Note on I^K and I^K*-convergence in topological spaces
• Characterizations of Ideal Cluster Points