A Universal Property of the Takahashi Quasi-Dual
1972 ◽
Vol 24
(3)
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pp. 530-536
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Keyword(s):
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].
1996 ◽
Vol 48
(6)
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pp. 1273-1285
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2007 ◽
Vol 143
(1)
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pp. 25-39
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1969 ◽
Vol 21
◽
pp. 655-659
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1974 ◽
Vol 17
(3)
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pp. 274-284
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Keyword(s):
1968 ◽
Vol 9
(2)
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pp. 87-91
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Keyword(s):
2012 ◽
Vol 88
(1)
◽
pp. 113-122
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1967 ◽
Vol 7
(4)
◽
pp. 433-454
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Keyword(s):
1971 ◽
Vol 23
(3)
◽
pp. 413-420
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