Multiplicative Bijections of Semigroups of Interval-valued Continuous Functions
نویسنده
چکیده
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 −→ X and a continuous map p : X −→ (0,+∞) such that φ(f)(x) = f(μ(x)) for every f ∈ C(X, I) and x ∈ 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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