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...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
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 |
| LEADER | 01654nab a2200229 i 4500 | ||
|---|---|---|---|
| 001 | acta73900 | ||
| 005 | 20211115133348.0 | ||
| 008 | 211115s2020 hu o 0|| eng d | ||
| 022 | |a 2064-8316 | ||
| 024 | 7 | |a 10.14232/actasm-020-116-1 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Oka Hirokazu | |
| 245 | 1 | 0 | |a Semigroup operations which are distributive over a given semigroup operation on positive real numbers |h [elektronikus dokumentum] / |c Oka Hirokazu |
| 260 | |c 2020 | ||
| 300 | |a 493-502 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 86 No. 3-4 | |
| 520 | 3 | |a 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. | |
| 695 | |a Matematika | ||
| 700 | 0 | 1 | |a Miura Takeshi |e aut |
| 700 | 0 | 1 | |a Takahasi Sin-Ei |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/73900/1/math_086_numb_003-004_493-502.pdf |z Dokumentum-elérés |