Connecting Locally Compact Abelian Groups

Ed Enochs; Walt Gerlach

doi:10.2307/2044930

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Connecting Locally Compact Abelian Groups

Ed Enochs Walt Gerlach

Year: 1983 Journal: Proceedings of the American Mathematical Society Vol: 89 (2)Pages: 351-351 Publisher: American Mathematical Society

DOI: 10.2307/2044930

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Abstract

Those locally compact abelian groups having connected envelopes are characterized as those $G$ such that the dimension of ${\operatorname {Hom }}(G,R)$ over $R$ is finite (where $R$ is the field of real numbers).

Keywords:

Abelian group Locally compact space Mathematics Elementary abelian group Rank of an abelian group Pure mathematics Field (mathematics) G-module Dimension (graph theory) Discrete mathematics

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Topics

Advanced Topology and Set Theory

Physical Sciences → Mathematics → Geometry and Topology

advanced mathematical theories

Physical Sciences → Mathematics → Mathematical Physics

Mathematical Dynamics and Fractals

Physical Sciences → Mathematics → Mathematical Physics

Connecting Locally Compact Abelian Groups

Abstract

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