Multiplicative bijections of semigroups of interval-valued continuous functions
| dc.creator | Araujo, Jesus | |
| dc.date | 2007-10-23 | |
| dc.date | 2007-12-13 | |
| dc.date.accessioned | 2026-07-07T08:48:45Z | |
| dc.date.available | 2026-07-07T08:48:45Z | |
| dc.description | We characterize all compact and Hausdorff spaces $X$ which satisfy that for every multiplicative bijection $ϕ$ on $C(X, I)$, there exist a homeomorphism $μ: X \to X$ and a continuous map $p: X \to (0, +\infty)$ such that $$ϕ(f) (x) = f(μ(x))^{p(x)}$$ for every $f \in C(X,I)$ and $x \in X$. This allows us to disprove a conjecture of Marovt (Proc. Amer. Math. Soc. {\bf 134} (2006), 1065-1075). Some related results on other semigroups of functions are also given. | |
| dc.description | 9 pages. No figures. Accepted for publication | |
| dc.identifier | https://arxiv.org/abs/0710.4347 | |
| dc.identifier | http://arxiv.org/abs/0710.4347 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144056 | |
| dc.subject | Functional Analysis | |
| dc.subject | General Topology | |
| dc.subject | 46J10; 46E05; 54D35 | |
| dc.title | Multiplicative bijections of semigroups of interval-valued continuous functions | |
| dc.type | text |