Subgroups of products of locally compact groups
Subgroups of products of locally compact groups
Summary: A topological group \(G\) is said to be locally \(q\)-minimal if there exists a neighbourhood \(V\) of the identity of \(G\) such that whenever \(H\) is a Hausdorff group and \(f:G\to H\) is a continuous surjective homomorphism with \(f(V)\) a neighbourhood of 1 in \(H\), then \(f\) is open. Locally compact groups are locally \(q\)-minimal. It is shown that under certain circumstances complete locally \(q\)-minimal groups are locally compact. This occurs for subgroups of products of locally compact groups in two cases: a) for products of locally compact abelian groups; b) for connected subgroups of products of locally compact MAP groups. It is also shown that ``MAP'' cannot be removed.
- University of Udine Italy
locally compact group; q-locally minimal group; locally minimal group, General properties and structure of locally compact groups, General properties and structure of LCA groups, Unitary representations of locally compact groups, Locally compact group, minimal group, open mapping theorem, Topological groups (topological aspects)
locally compact group; q-locally minimal group; locally minimal group, General properties and structure of locally compact groups, General properties and structure of LCA groups, Unitary representations of locally compact groups, Locally compact group, minimal group, open mapping theorem, Topological groups (topological aspects)
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