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Note on Linearly Compact Abelian Groups

Published online by Cambridge University Press:  09 April 2009

L. Fuchs
L. Fuchs
Affiliation:
University of Miami Coral Gables, Florida, U.S.A.
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By a group A is meant throughout an additively written abelian group. A is said to have linear topology if there is a system of subgroups Ui (i∈I) of A such that, for a ∈ A, the cosets a+Ui(i∈I) form a fundamental system of neighborhoods of a. The group operations are continuous in any linear topology; the topologies are always assumed to be Hausdorff, that is, ∩iUi = 0. A linearly compact group is a group A with a linear topology such that if aj+Aj (j∈I) is a system of cosets modulo closed subgroups Aj with the finite intersection property (i.e. any finite number of aj+Aj have a non-void intersection), then the intersection ∩j(aj+Aj) of all of them is not empty.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 3-4 , May 1969 , pp. 433 - 440
Copyright
Copyright © Australian Mathematical Society 1969

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