Journal of Lie Theory 18 (2008), No. 1, 193--203
Copyright Heldermann Verlag 2008
The Role of Real Characters in the Pontryagin Duality of Topological Abelian Groups
Sergio Ardanza-Trevijano
Dep. Física y Matemática Apl., Universidad de Navarra, C/ Irunlarrea S.N., 31080 Pamplona, Spain
sardanza@unav.es
María Jesús Chasco
Dep. Física y Matemática Apl., Universidad de Navarra, C/ Irunlarrea S.N., 31080 Pamplona, Spain
mjchasco@unav.es
Xabier Domínguez
Dep. Métodos Matemáticos y de Representación, Universidad de A Coruña, Campus de Elviña, 15071 A Coruña, Spain
xdominguez@udc.es
We study the role that real characters play in the context of Pontryagin duality of topological abelian groups. Among other problems, we show how the existence of enough real characters to separate points is related with the density of the arc-component of the dual group. This is exploited to study the arc-component of groups of continuous maps into T.
Keywords: Pontryagin duality, real character, one-parameter subgroup, arc-component, exponential function.
MSC: 22A05, 22D35
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