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A Universal Property of the Takahashi Quasi-Dual

Published online by Cambridge University Press:  20 November 2018

Detlev Poguntke*
Affiliation:
Universität Bielefeld, Bielefeld, West Germany
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Topological group always means Hausdorff topological group, homomorphism (isomorphism) between topological groups always means continuous homomorphism (homeomorphic isomorphism). For a topological group G, the topological commutator subgroup (the closure of the algebraic commutator subgroup) is denoted by G’. For each locally compact group G, Takahashi has constructed a locally compact group GT (called the Takahashi quasi-dual) and a homomorphism G → GT such that GT is maximally almost periodic, and GT is compact. The category of all locally compact groups with these two properties is denoted by [TAK]. Takahashi's duality theorem states that GGT is an isomorphism if G ∊ [TAK].

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1972

References

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