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Locally compact products and coproducts in categories of topological groups
Published online by Cambridge University Press: 17 April 2009
Abstract
In the category of locally compact groups not all families of groups have a product. Precisely which families do have a product and a description of the product is a corollary of the main theorem proved here. In the category of locally compact abelian groups a family {Gj; j ∈ J} has a product if and only if all but a finite number of the Gj are of the form Kj × Dj, where Kj is a compact group and Dj is a discrete torsion free group. Dualizing identifies the families having coproducts in the category of locally compact abelian groups and so answers a question of Z. Semadeni.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 17 , Issue 3 , December 1977 , pp. 401 - 417
- Copyright
- Copyright © Australian Mathematical Society 1977
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