## Multiplicative bijections of semigroups of interval-valued continuous functions

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- by Jesús Araujo
- Proc. Amer. Math. Soc.
**137**(2009), 171-178 - DOI: https://doi.org/10.1090/S0002-9939-08-09448-3
- Published electronically: July 1, 2008
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## Abstract:

We characterize all compact and Hausdorff spaces $X$ which satisfy the condition that for every multiplicative bijection $\varphi$ on $C(X, I)$, there exist a homeomorphism $\mu : X \longrightarrow X$ and a continuous map $p: X \longrightarrow (0, +\infty )$ such that \[ \varphi (f) (x) = f(\mu (x))^{p(x)}\] for every $f \in C(X,I)$ and $x \in X$. This allows us to disprove a conjecture of Marovt (Proc. Amer. Math. Soc.**134**(2006), 1065-1075). Some related results on other semigroups of functions are also given.

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## Bibliographic Information

**Jesús Araujo**- Affiliation: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Facultad de Ciencias, Avda. de los Castros, s. n., E-39071 Santander, Spain
- Email: araujoj@unican.es
- Received by editor(s): October 26, 2007
- Received by editor(s) in revised form: December 10, 2007
- Published electronically: July 1, 2008
- Additional Notes: This research was partially supported by the Spanish Ministry of Science and Education (Grant number MTM2006-14786).
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 171-178 - MSC (2000): Primary 46J10; Secondary 46E05, 54D35
- DOI: https://doi.org/10.1090/S0002-9939-08-09448-3
- MathSciNet review: 2439438