Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4660954 | Topology and its Applications | 2006 | 7 Pages |
Abstract
We prove that, when G is a group equipped with a Baire and metrizable topology, if there is a second category dense subset S of G such that the right translations ρs and ρs−1 are continuous for all s∈S and each left translation λs, s∈G, is almost-continuous (defined below) on a residual subset of G, then G is a topological group. Among other consequences, this yields that when G is a second countable locally compact right topological group, its topological centre is a topological group.
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