区间值连续函数半群的乘法双射
Multiplicative bijections of semigroups of interval-valued continuous functions
摘要：
本文刻划了所有紧Hausdorff空间$X$，满足对$C(X, I)$上的每一个乘法双射$ϕ$，存在一个同胚$μ: X \to X$和一个连续映射$p: X \to (0, +\infty)$，使得对每一个$f \in C(X,I)$和$x \in X$，都有$$ϕ(f) (x) = f(μ(x))^{p(x)}$$.这使我们能够反驳Marovt的一个猜想（Proc. Amer. Math. Soc. { \bf 134}（2006），1065-1075）。对其它函数半群也给出了相关结果。
英文摘要：
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.
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