On redundancy, separation and connectedness in multiset topological spaces

Rajish Kumar P; Sunil Jacob John; Rajish Kumar P; Sunil Jacob John

doi:10.3934/math.2020164

AIMS Mathematics

2020, Volume 5, Issue 3: 2484-2499. doi: 10.3934/math.2020164

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Research article

On redundancy, separation and connectedness in multiset topological spaces

Rajish Kumar P ^,,
Sunil Jacob John

Department of Mathematics, National Institute of Technology Calicut, Calicut, Kerala, India, Pin-673601

Received: 27 December 2019 Accepted: 27 February 2020 Published: 09 March 2020
MSC : 54A05, 54A10

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.
- multiset,
- M-topology,
- subspace M-topology,
- M-connectedness
Citation: Rajish Kumar P, Sunil Jacob John. On redundancy, separation and connectedness in multiset topological spaces[J]. AIMS Mathematics, 2020, 5(3): 2484-2499. doi: 10.3934/math.2020164

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Abstract

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.

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