2024-03-29T10:38:09Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/494772022-11-30T18:34:31Zcom_10234_7037com_10234_9col_10234_8635
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Ferrer González, María Vicenta
author
Hernández, Salvador
author
Ródenas Camacho, Ana María
author
2010
Let C(X,T{double-struck}) be the group of continuous functions of a compact Hausdorff space X to the unit circle of the complex plane T{double-struck} with the pointwise multiplication as the composition law. We investigate how the structure of C(X,T{double-struck}) determines the topology of X. In particular, which group isomorphisms H between the groups C(X,T{double-struck}) and C(Y,T{double-struck}) 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{double-struck}) 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. © 2009 Elsevier B.V.
Topology and its Applications, 157, 8, p. 1395-1403
1668641
http://hdl.handle.net/10234/49477
http://dx.doi.org/10.1016/j.topol.2009.04.069
Automatic continuity
Banach-Stone map
Dual group
Group homomorphisms
Group-valued continuous function
Pontryagin-van Kampen duality
Automatic continuity of biseparating homomorphisms defined between groups of continuous functions