The Role of Real Characters in the Pontryagin Duality of Topological Abelian Groups

S. Ardanza-Trevijano; M. J. Chasco; X. Domínguez

doi:10.5802/jolt.489

S. Ardanza-Trevijano; M. J. Chasco; X. Domínguez

Journal of Lie Theory, Volume 18 (2008) no. 1, pp. 193-203

Abstract

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.

Zbl

DOI: 10.5802/jolt.489

Classification: 22A05, 22D35
Keywords: Pontryagin duality, real character, one-parameter subgroup, arc-component, exponential function

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     title = {The {Role} of {Real} {Characters} in the {Pontryagin} {Duality} of {Topological} {Abelian} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {193--203},
     year = {2008},
     volume = {18},
     number = {1},
     doi = {10.5802/jolt.489},
     zbl = {1151.22003},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.489/}
}

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S. Ardanza-Trevijano; M. J. Chasco; X. Domínguez. The Role of Real Characters in the Pontryagin Duality of Topological Abelian Groups. Journal of Lie Theory, Volume 18 (2008) no. 1, pp. 193-203. doi: 10.5802/jolt.489

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