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Homomorphisms with respect to a function |
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| Authors: | Karim Boulabiar Foued Gdara |
| Institution: | 1. Département de Mathématiques, Faculté des Sciences de Tunis, Université Tunis-El Manar, 2092, Tunis, Tunisia 2. Département de Mathématiques, Institut Préparatoire aux Etudes d’Ingénieurs de Nabeul, Université de Carthage, 8000, Nabeul, Tunisia |
| Abstract: | Let X be a realcompact space and ${H:C(X)\rightarrow\mathbb{R}}$ be an identity and order preserving group homomorphism. It is shown that H is an evaluation at some point of X if and only if there is ${\varphi\in C(\mathbb{R})}$ with ${\varphi(r)>\varphi(0)}$ for all ${r\in\mathbb{R}-\{0\}}$ for which ${H\circ\varphi=\varphi\circ H}$ . This extends (and unifies) classical results by Hewitt and Shirota. |
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