A short note on coproducts of Abelian pro-Lie groups

Author:

Herfort WolfgangORCID,Hofmann Karl H.,Russo Francesco G.ORCID

Abstract

AbstractThe notion of conditional coproduct of a family of abelian pro-Lie groups in the category of abelian pro-Lie groups is introduced. It is shown that the cartesian product of an arbitrary family of abelian pro-Lie groups can be characterized by the universal property of the conditional coproduct.

Funder

TU Wien

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Reference6 articles.

1. Hofmann, K.H., Morris, S.A.: The Lie Theory of Connected Pro-Lie Groups. A Structure Theory for Pro-Lie Algebras, Pro-Lie Groups, and Connected Locally Compact Groups. EMS Tracts in Mathematics, vol. 2. European Mathematical Society (EMS), Zürich (2007)

2. Hofmann, K.H., Morris, S.A.: The Structure of Compact Groups. A Primer for the Student—A Handbook for the Expert. De Gruyter Studies in Mathematics, 3rd edn, vol. 25. De Gruyter, Berlin (2013)

3. Hofmann, K.H., Morris, S.A.: Locally compact products and coproducts in categories of topological groups. Bull. Aust. Math. Soc. 17, 401–417 (1977)

4. Kelley, J.L.: General Topology. Graduate Texts in Mathematics, No. 27. Reprint of the 1955 edition [Van Nostrand, Toronto, Ont.]. Springer-Verlag, New York-Berlin (1975)

5. Neukirch, J.: Freie Produkte pro-endlicher Gruppen und ihre Kohomologie. Arch. Math. 22, 337–357 (1971)

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1. Neat locally compact abelian p-groups;Mathematische Annalen;2024-03-25

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