On redundancy, separation and connectedness in multiset topological spaces

This paper makes an attempt to study M-topology as a novel structure and emphasizes its importance by projecting how it differs from general topology. Primarily, the issue of redundancy in Mtopology is addressed by pointing out the importance of complementation with appropriate examples. Unlike gene...

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Bibliographic Details
Main Authors: Rajish Kumar P, Sunil Jacob John
Format: Article
Language:English
Published: AIMS Press 2020-03-01
Series:AIMS Mathematics
Subjects:
Online Access:https://www.aimspress.com/article/10.3934/math.2020164/fulltext.html
Description
Summary:This paper makes an attempt to study M-topology as a novel structure and emphasizes its importance by projecting how it differs from general topology. Primarily, the issue of redundancy in Mtopology is addressed by pointing out the importance of complementation with appropriate examples. Unlike general topology, M-topology induces two subspace M-topologies on a submset. In general topology, these two definitions of the subspace topologies coincide. The situations in which these two subspace M-topologies coincide are also analyzed for the purpose. Furthermore, two types of Mconnectedness and M-separations in M-topology are introduced and it is proved that neither of which implies the other.
ISSN:2473-6988