Further aspects of I K-convergence in topological spaces

Ankur Sharmah

India

Tezpur University

Department of Mathematical Sciences

Debajit Hazarika

India

Tezpur University

Professor, Department of Mathematical Sciences

Department of Mathematical Sciences

Submitted: 2021-01-01

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Accepted: 2021-03-26

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Published: 2021-10-01

DOI: https://doi.org/10.4995/agt.2021.14868
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Keywords:

I-convergence, I K-convergence, I K∗ -convergence, I K-sequential space, I K-cluster point

Supporting agencies:

University Grants Comission (UGC) research fellowship vide UGCRef. No.

1115/(CSIR-UGC NET DEC. 2017)

India

Abstract:

In this paper, we obtain some results on the relationships between different ideal 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.
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