Topological and ditopological unosemigroups
In this paper we introduce and study a new topologo-algebraic structure called a (di)topological unosemigroup. This is a topological semigroup endowed with continuous unary operations of left and right units (which have certain continuous division property called the dicontinuity). We show that the...
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| Format: | Article |
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Ivan Franko National University of Lviv
2013-07-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/texts/2013/39_2/119-133.pdf |
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| author | T. Banakh I. Pastukhova |
| author_facet | T. Banakh I. Pastukhova |
| author_sort | T. Banakh |
| collection | DOAJ |
| description | In this paper we introduce and study a new topologo-algebraic structure called a (di)topological unosemigroup. This is a topological semigroup endowed with continuous unary operations of left and right units (which have certain continuous division property called the dicontinuity). We show that the class of ditopological unosemigroups contains all topological groups, all topological semilattices, all uniformizable topological unosemigroups, all compact topological unosemigroups, and is closed under the operations of taking subunosemigroups, Tychonoff product, reduced product, semidirect product, and the Hartman-Mycielski extension. |
| format | Article |
| id | doaj-art-b130dc98152b4f4f813fcd06659216f7 |
| institution | DOAJ |
| issn | 1027-4634 |
| language | deu |
| publishDate | 2013-07-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-b130dc98152b4f4f813fcd06659216f72025-08-20T02:51:39ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342013-07-01392119133Topological and ditopological unosemigroupsT. BanakhI. PastukhovaIn this paper we introduce and study a new topologo-algebraic structure called a (di)topological unosemigroup. This is a topological semigroup endowed with continuous unary operations of left and right units (which have certain continuous division property called the dicontinuity). We show that the class of ditopological unosemigroups contains all topological groups, all topological semilattices, all uniformizable topological unosemigroups, all compact topological unosemigroups, and is closed under the operations of taking subunosemigroups, Tychonoff product, reduced product, semidirect product, and the Hartman-Mycielski extension.http://matstud.org.ua/texts/2013/39_2/119-133.pdftopological semigroupunosemigroupditopological unosemigroup |
| spellingShingle | T. Banakh I. Pastukhova Topological and ditopological unosemigroups Математичні Студії topological semigroup unosemigroup ditopological unosemigroup |
| title | Topological and ditopological unosemigroups |
| title_full | Topological and ditopological unosemigroups |
| title_fullStr | Topological and ditopological unosemigroups |
| title_full_unstemmed | Topological and ditopological unosemigroups |
| title_short | Topological and ditopological unosemigroups |
| title_sort | topological and ditopological unosemigroups |
| topic | topological semigroup unosemigroup ditopological unosemigroup |
| url | http://matstud.org.ua/texts/2013/39_2/119-133.pdf |
| work_keys_str_mv | AT tbanakh topologicalandditopologicalunosemigroups AT ipastukhova topologicalandditopologicalunosemigroups |