Exploring Maximal and Minimal Open Submsets in M-Topology: A Comprehensive Analysis
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Keywords:
Multiset, Multiset topology, M-topology, maximal open sets, minimal open sets, connectednessAbstract
Topological structures defined in the context of multisets, a set that allows multiple occurrences of objects, are referred to as M-topological spaces. This article introduces the concept of maximal and minimal open submsets in M-topology. The role of whole elements and part elements in maximal open and minimal open submsets and their uniqueness, together with the topological situation in which an open submset becomes both maximal open and minimal open, is analysed. Some conditions for disconnectedness in M-topologyical spaces are obtained in light of the fact that the existence of a non-empty proper clopen submset is not enough to establish the disconnectedness of an M-topologyical space.
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