Categorically Closed Topological Groups
Let C → be a category whose objects are semigroups with topology and morphisms are closed semigroup relations, in particular, continuous homomorphisms. An object X of the category C → is called C → -closed if for each morphism Φ ⊂ X × Y in the category C → the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-07-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/6/3/23 |
| _version_ | 1819206619429339136 |
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| author | Taras Banakh |
| author_facet | Taras Banakh |
| author_sort | Taras Banakh |
| collection | DOAJ |
| description | Let C → be a category whose objects are semigroups with topology and morphisms are closed semigroup relations, in particular, continuous homomorphisms. An object X of the category C → is called C → -closed if for each morphism Φ ⊂ X × Y in the category C → the image Φ ( X ) = { y ∈ Y : ∃ x ∈ X ( x , y ) ∈ Φ } is closed in Y. In the paper we survey existing and new results on topological groups, which are C → -closed for various categories C → of topologized semigroups. |
| first_indexed | 2024-12-23T05:10:29Z |
| format | Article |
| id | doaj.art-e92c81d7675f4b07867ab15d6fbe593f |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-23T05:10:29Z |
| publishDate | 2017-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-e92c81d7675f4b07867ab15d6fbe593f2022-12-21T17:58:59ZengMDPI AGAxioms2075-16802017-07-01632310.3390/axioms6030023axioms6030023Categorically Closed Topological GroupsTaras Banakh0Faculty of Mechanics and Mathematics, Ivan Franko National University, 79000 Lviv, UkraineLet C → be a category whose objects are semigroups with topology and morphisms are closed semigroup relations, in particular, continuous homomorphisms. An object X of the category C → is called C → -closed if for each morphism Φ ⊂ X × Y in the category C → the image Φ ( X ) = { y ∈ Y : ∃ x ∈ X ( x , y ) ∈ Φ } is closed in Y. In the paper we survey existing and new results on topological groups, which are C → -closed for various categories C → of topologized semigroups.https://www.mdpi.com/2075-1680/6/3/23topological groupparatopological grouptopological semigroupabsolutely closed topological grouptopological group of compact exponent |
| spellingShingle | Taras Banakh Categorically Closed Topological Groups Axioms topological group paratopological group topological semigroup absolutely closed topological group topological group of compact exponent |
| title | Categorically Closed Topological Groups |
| title_full | Categorically Closed Topological Groups |
| title_fullStr | Categorically Closed Topological Groups |
| title_full_unstemmed | Categorically Closed Topological Groups |
| title_short | Categorically Closed Topological Groups |
| title_sort | categorically closed topological groups |
| topic | topological group paratopological group topological semigroup absolutely closed topological group topological group of compact exponent |
| url | https://www.mdpi.com/2075-1680/6/3/23 |
| work_keys_str_mv | AT tarasbanakh categoricallyclosedtopologicalgroups |