Automatic continuity of biseparating homomorphisms defined between groups of continuous functions |
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Authors: | Ma Vicenta Ferrer Ana María Ródenas |
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Institution: | Departamento de Matemáticas, Universidad Jaume I, 12071 Castellón, Spain |
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Abstract: | Let C(X,T) be the group of continuous functions of a compact Hausdorff space X to the unit circle of the complex plane T with the pointwise multiplication as the composition law. We investigate how the structure of C(X,T) determines the topology of X. In particular, which group isomorphisms H between the groups C(X,T) and C(Y,T) imply the existence of a continuous map h of Y into X such that H is canonically represented by h. Among other results, it is proved that C(X,T) determines X module a biseparating group isomorphism and, when X is first countable, the automatic continuity and representation as Banach-Stone maps for biseparating group isomorphisms is also obtained. |
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Keywords: | 22A10 22B99 22C05 43A40 54H11 54D30 54E35 |
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