Automatic continuity of biseparating homomorphisms defined between groups of continuous functions
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Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
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http://dx.doi.org/10.1016/j.topol.2009.04.069 |
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Title
Automatic continuity of biseparating homomorphisms defined between groups of continuous functionsDate
2010Publisher
ElsevierISSN
1668641Bibliographic citation
Topology and its Applications, 157, 8, p. 1395-1403Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
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 ... [+]
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. [-]
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