Mal'tsev and retral spaces
A space <em>X</em> is Mal&apos;tsev if there exists a continuous map <em>M: X<sup>3</sup> → X </em> such that <em>M(x, y, y) = x = M(y, y, x)</em>. A space <em>X</em> is retral if it is a retract of a topological group. Every retral...
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| Format: | Journal article |
| Language: | English |
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Elsevier
1997
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| _version_ | 1826280899366354944 |
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| author | Gartside, P Reznichenko, E Sipacheva, O |
| author_facet | Gartside, P Reznichenko, E Sipacheva, O |
| author_sort | Gartside, P |
| collection | OXFORD |
| description | A space <em>X</em> is Mal&apos;tsev if there exists a continuous map <em>M: X<sup>3</sup> → X </em> such that <em>M(x, y, y) = x = M(y, y, x)</em>. A space <em>X</em> is retral if it is a retract of a topological group. Every retral space is Mal&apos;tsev. General methods for constructing Mal&apos;tsev and retral spaces are given. An example of a Mal&apos;tsev space which is not retral is presented. An example of a Lindelöf topological group with cellularity the continuum is presented. Constraints on the examples are examined. |
| first_indexed | 2024-03-07T00:20:40Z |
| format | Journal article |
| id | oxford-uuid:7c6d39b2-4818-43a4-a177-f4f76e411514 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:20:40Z |
| publishDate | 1997 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:7c6d39b2-4818-43a4-a177-f4f76e4115142022-03-26T20:57:03ZMal'tsev and retral spacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7c6d39b2-4818-43a4-a177-f4f76e411514Algebraic topologyEnglishOxford University Research Archive - ValetElsevier1997Gartside, PReznichenko, ESipacheva, OA space <em>X</em> is Mal&apos;tsev if there exists a continuous map <em>M: X<sup>3</sup> → X </em> such that <em>M(x, y, y) = x = M(y, y, x)</em>. A space <em>X</em> is retral if it is a retract of a topological group. Every retral space is Mal&apos;tsev. General methods for constructing Mal&apos;tsev and retral spaces are given. An example of a Mal&apos;tsev space which is not retral is presented. An example of a Lindelöf topological group with cellularity the continuum is presented. Constraints on the examples are examined. |
| spellingShingle | Algebraic topology Gartside, P Reznichenko, E Sipacheva, O Mal'tsev and retral spaces |
| title | Mal'tsev and retral spaces |
| title_full | Mal'tsev and retral spaces |
| title_fullStr | Mal'tsev and retral spaces |
| title_full_unstemmed | Mal'tsev and retral spaces |
| title_short | Mal'tsev and retral spaces |
| title_sort | mal tsev and retral spaces |
| topic | Algebraic topology |
| work_keys_str_mv | AT gartsidep maltsevandretralspaces AT reznichenkoe maltsevandretralspaces AT sipachevao maltsevandretralspaces |