Strong semilattices of topological groups
The notion of partial groups and their basic properties have been given in [1,2]. In this paper, we introduce the concept of topological partial groups and discuss some of their basic properties. So, the category of topological partial groups Tpg, as objects, and the homomorphisms of topological par...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-10-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X16300074 |
| _version_ | 1819135814461816832 |
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| author | A.M. Abd-Allah A.I. Aggour A. Fathy |
| author_facet | A.M. Abd-Allah A.I. Aggour A. Fathy |
| author_sort | A.M. Abd-Allah |
| collection | DOAJ |
| description | The notion of partial groups and their basic properties have been given in [1,2]. In this paper, we introduce the concept of topological partial groups and discuss some of their basic properties. So, the category of topological partial groups Tpg, as objects, and the homomorphisms of topological partial groups, as arrows, have some deficiencies. To get over these deficiencies, we introduced the category of locally compact partial groups denoted by Lcpg. Finally, we introduced the category of strong semilattices of topological groups denoted by Sstg. |
| first_indexed | 2024-12-22T10:25:04Z |
| format | Article |
| id | doaj.art-c4b3c044b2264d7c9042773058522218 |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-22T10:25:04Z |
| publishDate | 2016-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-c4b3c044b2264d7c90427730585222182022-12-21T18:29:31ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2016-10-0124459760210.1016/j.joems.2016.03.003Strong semilattices of topological groupsA.M. Abd-AllahA.I. AggourA. FathyThe notion of partial groups and their basic properties have been given in [1,2]. In this paper, we introduce the concept of topological partial groups and discuss some of their basic properties. So, the category of topological partial groups Tpg, as objects, and the homomorphisms of topological partial groups, as arrows, have some deficiencies. To get over these deficiencies, we introduced the category of locally compact partial groups denoted by Lcpg. Finally, we introduced the category of strong semilattices of topological groups denoted by Sstg.http://www.sciencedirect.com/science/article/pii/S1110256X16300074Partial groupTopological groupIdentification mapStrong semilatticePartial group homomorphism |
| spellingShingle | A.M. Abd-Allah A.I. Aggour A. Fathy Strong semilattices of topological groups Journal of the Egyptian Mathematical Society Partial group Topological group Identification map Strong semilattice Partial group homomorphism |
| title | Strong semilattices of topological groups |
| title_full | Strong semilattices of topological groups |
| title_fullStr | Strong semilattices of topological groups |
| title_full_unstemmed | Strong semilattices of topological groups |
| title_short | Strong semilattices of topological groups |
| title_sort | strong semilattices of topological groups |
| topic | Partial group Topological group Identification map Strong semilattice Partial group homomorphism |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X16300074 |
| work_keys_str_mv | AT amabdallah strongsemilatticesoftopologicalgroups AT aiaggour strongsemilatticesoftopologicalgroups AT afathy strongsemilatticesoftopologicalgroups |