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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-03-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020164/fulltext.html |
| _version_ | 1818923229271556096 |
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| author | Rajish Kumar P Sunil Jacob John |
| author_facet | Rajish Kumar P Sunil Jacob John |
| author_sort | Rajish Kumar P |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T02:06:07Z |
| format | Article |
| id | doaj.art-e50087388c624c279808c203ed8d13b7 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-20T02:06:07Z |
| publishDate | 2020-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-e50087388c624c279808c203ed8d13b72022-12-21T19:57:11ZengAIMS PressAIMS Mathematics2473-69882020-03-01532484249910.3934/math.2020164On redundancy, separation and connectedness in multiset topological spacesRajish Kumar P0Sunil Jacob John1Department of Mathematics, National Institute of Technology Calicut, Calicut, Kerala, India, Pin-673601Department of Mathematics, National Institute of Technology Calicut, Calicut, Kerala, India, Pin-673601This 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.https://www.aimspress.com/article/10.3934/math.2020164/fulltext.htmlmultisetm-topologysubspace m-topologym-connectedness |
| spellingShingle | Rajish Kumar P Sunil Jacob John On redundancy, separation and connectedness in multiset topological spaces AIMS Mathematics multiset m-topology subspace m-topology m-connectedness |
| title | On redundancy, separation and connectedness in multiset topological spaces |
| title_full | On redundancy, separation and connectedness in multiset topological spaces |
| title_fullStr | On redundancy, separation and connectedness in multiset topological spaces |
| title_full_unstemmed | On redundancy, separation and connectedness in multiset topological spaces |
| title_short | On redundancy, separation and connectedness in multiset topological spaces |
| title_sort | on redundancy separation and connectedness in multiset topological spaces |
| topic | multiset m-topology subspace m-topology m-connectedness |
| url | https://www.aimspress.com/article/10.3934/math.2020164/fulltext.html |
| work_keys_str_mv | AT rajishkumarp onredundancyseparationandconnectednessinmultisettopologicalspaces AT suniljacobjohn onredundancyseparationandconnectednessinmultisettopologicalspaces |