Geodesic
A Universal Property of the Takahashi Quasi-Dual
Canadian journal of mathematics, Tome 24 (1972) no. 3, pp. 530-536

Voir la notice de l'article provenant de la source Cambridge University Press

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 G → GT is an isomorphism if G ∊ [TAK]. 
Poguntke, Detlev. A Universal Property of the Takahashi Quasi-Dual. Canadian journal of mathematics, Tome 24 (1972) no. 3, pp. 530-536. doi: 10.4153/CJM-1972-045-2
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