On continuity of homomorphisms between topological Clifford semigroups
Generalizing an old result of Bowman we prove that a homomorphism $f:X\to Y$ between topological Clifford semigroups is continuous if • the idempotent band $E_X=\{x\in X:xx=x\}$ of $X$ is a $V$-semilattice; • the topological Clifford semigroup $Y$ is ditopological; • the restriction $f|E_...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2014-07-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/1343 |
| Summary: | Generalizing an old result of Bowman we prove that a homomorphism $f:X\to Y$ between topological Clifford semigroups is continuous if
• the idempotent band $E_X=\{x\in X:xx=x\}$ of $X$ is a $V$-semilattice;
• the topological Clifford semigroup $Y$ is ditopological;
• the restriction $f|E_X$ is continuous;
• for each subgroup $H\subset X$ the restriction $f|H$ is continuous. |
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| ISSN: | 2075-9827 2313-0210 |