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Continuous Duality of Limits and Colimits of Topological Abelian Groups

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Abstract

In the category Cgp of convergence groups, the continuous dual Γ c ( ·) is a left adjoint and takes colimits to limits in Cgp. In general, limits are not taken to colimits. In this paper we show that, if we restrict ourselves to limits of topological groups, then reduced projective limits are carried to inductive limits in Cgp. As a consequence of this we show that the inductive limit in Cgp of locally compact topological groups is reflexive if it is separated.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Mount Allison University, Sackville, NB, Canada, E4L 1E6

    R. Beattie

  2. Fakultät für Mathematik und Informatik, Universität Mannheim, Mannheim, Germany

    H.-P. Butzmann

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  1. R. Beattie
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  2. H.-P. Butzmann
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Correspondence to R. Beattie.

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Beattie, R., Butzmann, HP. Continuous Duality of Limits and Colimits of Topological Abelian Groups. Appl Categor Struct 16, 535–549 (2008). https://doi.org/10.1007/s10485-007-9112-5

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  • DOI: https://doi.org/10.1007/s10485-007-9112-5

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