Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-25T22:08:24.706Z Has data issue: false hasContentIssue false

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Herrlich, H., Topologische Reflexionen und Coreflexionen (Berlin, 1968).Google Scholar
2. Heyer, H., Dualität lokalkompakter Gruppen (Berlin, 1970).Google Scholar
3. Pontryagin, L. S., Topologische Gruppen (Leipzig, 1958).Google Scholar
4. Suzuki, K., Notes on the duality theorem of noncommutative topological groups, Tôhoku Math. J. 15 (1963), 182186 Google Scholar
5. Takahashi, S., A duality theorem for representable locally compact groups with compact commutator subgroup, Tôhoku Math. J. 4 (1952), 115121.Google Scholar
6. Tannaka, T., Über den Dualitätssatz der nichikommutativen topologischen Gruppen, Tôhoku Math. J. 53 (1938), 112.Google Scholar