Series with Commuting Terms in Topologized Semigroups
We show that the following general version of the Riemann–Dirichlet theorem is true: if every rearrangement of a series with pairwise commuting terms in a Hausdorff topologized semigroup converges, then its sum range is a singleton.
| Autors principals: | , , |
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| Format: | Article |
| Idioma: | English |
| Publicat: |
MDPI AG
2021-09-01
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| Col·lecció: | Axioms |
| Matèries: | |
| Accés en línia: | https://www.mdpi.com/2075-1680/10/4/237 |
| _version_ | 1827674108616245248 |
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| author | Alberto Castejón Eusebio Corbacho Vaja Tarieladze |
| author_facet | Alberto Castejón Eusebio Corbacho Vaja Tarieladze |
| author_sort | Alberto Castejón |
| collection | DOAJ |
| description | We show that the following general version of the Riemann–Dirichlet theorem is true: if every rearrangement of a series with pairwise commuting terms in a Hausdorff topologized semigroup converges, then its sum range is a singleton. |
| first_indexed | 2024-03-10T04:35:58Z |
| format | Article |
| id | doaj.art-b51d1b8aa11e4c069a5f1e5b9e6c97c3 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T04:35:58Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-b51d1b8aa11e4c069a5f1e5b9e6c97c32023-11-23T03:48:48ZengMDPI AGAxioms2075-16802021-09-0110423710.3390/axioms10040237Series with Commuting Terms in Topologized SemigroupsAlberto Castejón0Eusebio Corbacho1Vaja Tarieladze2Departamento de Matemática Aplicada I, University of Vigo, 36310 Vigo, SpainDepartamento de Matemática Aplicada I, University of Vigo, 36310 Vigo, SpainMuskhelishvili Institute of Computational Mathematics, Georgian Technical University, Tbilisi 0159, GeorgiaWe show that the following general version of the Riemann–Dirichlet theorem is true: if every rearrangement of a series with pairwise commuting terms in a Hausdorff topologized semigroup converges, then its sum range is a singleton.https://www.mdpi.com/2075-1680/10/4/237semigroupgrouptopologypermutationconvergence |
| spellingShingle | Alberto Castejón Eusebio Corbacho Vaja Tarieladze Series with Commuting Terms in Topologized Semigroups Axioms semigroup group topology permutation convergence |
| title | Series with Commuting Terms in Topologized Semigroups |
| title_full | Series with Commuting Terms in Topologized Semigroups |
| title_fullStr | Series with Commuting Terms in Topologized Semigroups |
| title_full_unstemmed | Series with Commuting Terms in Topologized Semigroups |
| title_short | Series with Commuting Terms in Topologized Semigroups |
| title_sort | series with commuting terms in topologized semigroups |
| topic | semigroup group topology permutation convergence |
| url | https://www.mdpi.com/2075-1680/10/4/237 |
| work_keys_str_mv | AT albertocastejon serieswithcommutingtermsintopologizedsemigroups AT eusebiocorbacho serieswithcommutingtermsintopologizedsemigroups AT vajatarieladze serieswithcommutingtermsintopologizedsemigroups |