On topologies on the underlying set of a topological monoid induced by its unitary extensions
Extensions of a given topological monoid where all its unitary Cauchy filters converge, can induce di˙erent topologies on its underlying set. We study properties of these topologies and prove a condition under which the initial topology of this monoid is one of them.
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-04-01
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| Series: | Topological Algebra and its Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/taa-2020-0110 |
| _version_ | 1797848615507460096 |
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| author | Averbukh Boris G. |
| author_facet | Averbukh Boris G. |
| author_sort | Averbukh Boris G. |
| collection | DOAJ |
| description | Extensions of a given topological monoid where all its unitary Cauchy filters converge, can induce di˙erent topologies on its underlying set. We study properties of these topologies and prove a condition under which the initial topology of this monoid is one of them. |
| first_indexed | 2024-04-09T18:31:29Z |
| format | Article |
| id | doaj.art-fba4c15906fb428bbf5e8063bac81401 |
| institution | Directory Open Access Journal |
| issn | 2299-3231 |
| language | English |
| last_indexed | 2024-04-09T18:31:29Z |
| publishDate | 2022-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Topological Algebra and its Applications |
| spelling | doaj.art-fba4c15906fb428bbf5e8063bac814012023-04-11T17:07:20ZengDe GruyterTopological Algebra and its Applications2299-32312022-04-01101253510.1515/taa-2020-0110On topologies on the underlying set of a topological monoid induced by its unitary extensionsAverbukh Boris G.0Bauman Moscow State Technical University, department of mathematics, Moscow, Russian FederationExtensions of a given topological monoid where all its unitary Cauchy filters converge, can induce di˙erent topologies on its underlying set. We study properties of these topologies and prove a condition under which the initial topology of this monoid is one of them.https://doi.org/10.1515/taa-2020-0110topological monoidcauchy filtercompletion22a1554h10 |
| spellingShingle | Averbukh Boris G. On topologies on the underlying set of a topological monoid induced by its unitary extensions Topological Algebra and its Applications topological monoid cauchy filter completion 22a15 54h10 |
| title | On topologies on the underlying set of a topological monoid induced by its unitary extensions |
| title_full | On topologies on the underlying set of a topological monoid induced by its unitary extensions |
| title_fullStr | On topologies on the underlying set of a topological monoid induced by its unitary extensions |
| title_full_unstemmed | On topologies on the underlying set of a topological monoid induced by its unitary extensions |
| title_short | On topologies on the underlying set of a topological monoid induced by its unitary extensions |
| title_sort | on topologies on the underlying set of a topological monoid induced by its unitary extensions |
| topic | topological monoid cauchy filter completion 22a15 54h10 |
| url | https://doi.org/10.1515/taa-2020-0110 |
| work_keys_str_mv | AT averbukhborisg ontopologiesontheunderlyingsetofatopologicalmonoidinducedbyitsunitaryextensions |