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Compactness and subspace M-topologies

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Abstract

In this paper, we emphasize how M-topological concepts like closed sets, closure of submsets, etc., differ from similar concepts in general topology. Further, we discuss the open cover of a submset in two different subspace M-topologies and define two distinct types of compactness for a submset. Conditions in terms of counts are obtained for inducing open covers for a submset in both of the two subspace M-topologies. Further, a new concept of double compactness is introduced.

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Acknowledgements

The authors appreciate the editor’s and anonymous reviewers’ constructive remarks and suggestions, which helped us improve the paper substantially. Also, during the development of the manuscript, the first and second authors gratefully acknowledge DST, Government of India, for providing support to carry out this work under the scheme ’FIST’ (No. SR/FST/MS-I/2019/40).

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Calicut, Kerala, 673601, India

    P. Rajish Kumar & Sunil Jacob John

  2. Department of Mathematics, Tamralipta Mahavidyalaya (Vidyasagar University), Tamluk, Purba Medinipur, West Bengal, 721636, India

    Sovan Samanta

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  1. P. Rajish Kumar
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  2. Sunil Jacob John
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  3. Sovan Samanta
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Kumar, P.R., John, S.J. & Samanta, S. Compactness and subspace M-topologies. Soft Comput 26, 4115–4122 (2022). https://doi.org/10.1007/s00500-022-06863-w

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