Semigroup operations which are distributive over a given semigroup operation on positive real numbers
Let R+ be the space of positive real numbers with the ordinary topology and let ⋆ be an arbitrary cancellative continuous semigroup operation on R+ or some special noncancellative continuous semigroup operation on R+. We characterize the set D −1 ⋆ (R+) of all cancellative continuous semigroup opera...
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| Dokumentumtípus: | Cikk |
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2020
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| Sorozat: | Acta scientiarum mathematicarum
86 No. 3-4 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-020-116-1 |
| Online Access: | http://acta.bibl.u-szeged.hu/73900 |
| Tartalmi kivonat: | Let R+ be the space of positive real numbers with the ordinary topology and let ⋆ be an arbitrary cancellative continuous semigroup operation on R+ or some special noncancellative continuous semigroup operation on R+. We characterize the set D −1 ⋆ (R+) of all cancellative continuous semigroup operations on R+ which are distributive over ⋆ in terms of homeomorphism. As a consequence, it is shown that if ⋆ is homeomorphically isomorphic to the ordinary addition + on R+, any element of D −1 ⋆ (R+) is homeomorphically isomorphic to the ordinary multiplication on R+, and that if ⋆ is cancellative and not homeomorphically isomorphic to +, then D −1 ⋆ (R+) is empty. Moreover, if ⋆ is homeomorphically isomorphic to some special noncancellative continuous semigroup operation on R+, D −1 ⋆ (R+) is also shown to be empty. |
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| Terjedelem/Fizikai jellemzők: | 493-502 |
| ISSN: | 2064-8316 |