Hereditary Coreflective Subcategories in Certain Categories of Abelian Semitopological Groups
Let <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">A</mi> </semantics> </math> </inline-formula> be an epireflective subcategory of the category of all semitopological groups that consists only of abelia...
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MDPI AG
2019-07-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/8/3/85 |
| _version_ | 1819132204470501376 |
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| author | Veronika Pitrová |
| author_facet | Veronika Pitrová |
| author_sort | Veronika Pitrová |
| collection | DOAJ |
| description | Let <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">A</mi> </semantics> </math> </inline-formula> be an epireflective subcategory of the category of all semitopological groups that consists only of abelian groups. We describe maximal hereditary coreflective subcategories of <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">A</mi> </semantics> </math> </inline-formula> that are not bicoreflective in <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">A</mi> </semantics> </math> </inline-formula> in the case that the <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">A</mi> </semantics> </math> </inline-formula>-reflection of the discrete group of integers is a finite cyclic group, the group of integers with a topology that is not <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula>, or the group of integers with the topology generated by its subgroups of the form <inline-formula> <math display="inline"> <semantics> <mfenced separators="" open="〈" close="〉"> <msup> <mi>p</mi> <mi>n</mi> </msup> </mfenced> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> </mrow> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>p</mi> <mo>∈</mo> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> and <i>P</i> is a given set of prime numbers. |
| first_indexed | 2024-12-22T09:27:41Z |
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| id | doaj.art-7beb1e7b60fa4dd6bf0b4c8167f084cd |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-22T09:27:41Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-7beb1e7b60fa4dd6bf0b4c8167f084cd2022-12-21T18:31:03ZengMDPI AGAxioms2075-16802019-07-01838510.3390/axioms8030085axioms8030085Hereditary Coreflective Subcategories in Certain Categories of Abelian Semitopological GroupsVeronika Pitrová0Department of Mathematics, Faculty of Science, Jan Evangelista Purkyně University, České mládeže 8, 400 96 Ústí nad Labem, Czech RepublicLet <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">A</mi> </semantics> </math> </inline-formula> be an epireflective subcategory of the category of all semitopological groups that consists only of abelian groups. We describe maximal hereditary coreflective subcategories of <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">A</mi> </semantics> </math> </inline-formula> that are not bicoreflective in <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">A</mi> </semantics> </math> </inline-formula> in the case that the <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">A</mi> </semantics> </math> </inline-formula>-reflection of the discrete group of integers is a finite cyclic group, the group of integers with a topology that is not <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula>, or the group of integers with the topology generated by its subgroups of the form <inline-formula> <math display="inline"> <semantics> <mfenced separators="" open="〈" close="〉"> <msup> <mi>p</mi> <mi>n</mi> </msup> </mfenced> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> </mrow> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>p</mi> <mo>∈</mo> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> and <i>P</i> is a given set of prime numbers.https://www.mdpi.com/2075-1680/8/3/85semitopological groupabelian groupcoreflective subcategoryhereditary subcategory |
| spellingShingle | Veronika Pitrová Hereditary Coreflective Subcategories in Certain Categories of Abelian Semitopological Groups Axioms semitopological group abelian group coreflective subcategory hereditary subcategory |
| title | Hereditary Coreflective Subcategories in Certain Categories of Abelian Semitopological Groups |
| title_full | Hereditary Coreflective Subcategories in Certain Categories of Abelian Semitopological Groups |
| title_fullStr | Hereditary Coreflective Subcategories in Certain Categories of Abelian Semitopological Groups |
| title_full_unstemmed | Hereditary Coreflective Subcategories in Certain Categories of Abelian Semitopological Groups |
| title_short | Hereditary Coreflective Subcategories in Certain Categories of Abelian Semitopological Groups |
| title_sort | hereditary coreflective subcategories in certain categories of abelian semitopological groups |
| topic | semitopological group abelian group coreflective subcategory hereditary subcategory |
| url | https://www.mdpi.com/2075-1680/8/3/85 |
| work_keys_str_mv | AT veronikapitrova hereditarycoreflectivesubcategoriesincertaincategoriesofabeliansemitopologicalgroups |