Notes on duality theories of abelian groups

Details Notes on duality theories of abelian groups Notes on duality theories of abelian groups

2006-05-05

arxiv.org/abs/math/0605149v1

Mathematics

General Topology

v0.1: Contains only Chapter 1 and Appendix

Scientific paper

In this notebook, I present duality theory (or theories) of abelian groups with some categorical and categorical topological flavour. I consider writing this notebook as a longer-term project, and its current content and presentation is "under development." In other words, all questions, comments, suggestions, and criticism is more than usually welcome. In Chapter 1, which is the only more-or-less ready part, the evaluation homomorphism A --> A^^ (of a group A into its bidual A^^) is studied, with particular attention to quasi-convexity and special groups (compact, discrete, LCA) and subgroups (open, compact). The treatment of LCA groups is incomplete, but the ultimate goal is to make it as self-contained as possible.

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