Oka Hirokazu; Miura Takeshi; Takahasi Sin-Ei: Semigroup operations which are distributive over a given semigroup operation on positive real numbers. In: Acta scientiarum mathematicarum, (86) 3-4. pp. 493-502. (2020)
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Absztrakt (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.
| Mű típusa: | Cikk, tanulmány, mű |
|---|---|
| Rovatcím: | Analysis |
| Befoglaló folyóirat/kiadvány címe: | Acta scientiarum mathematicarum |
| Dátum: | 2020 |
| Kötet: | 86 |
| Szám: | 3-4 |
| ISSN: | 2064-8316 |
| Oldalak: | pp. 493-502 |
| Nyelv: | angol |
| Befoglaló mű URL: | http://acta.bibl.u-szeged.hu/73790/ |
| DOI: | 10.14232/actasm-020-116-1 |
| Kulcsszavak: | Matematika |
| Megjegyzések: | Bibliogr.: p. 501-502. ; összefoglalás angol nyelven |
| Feltöltés dátuma: | 2021. nov. 15. 13:33 |
| Utolsó módosítás: | 2021. nov. 15. 13:33 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/73900 |
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