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Note on Linearly Compact Abelian Groups

Published online by Cambridge University Press:  09 April 2009

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 (iI) of A such that, for aA, the cosets a+Ui(iI) 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 (jI) 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
Copyright
Copyright © Australian Mathematical Society 1969

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