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Continuity in topological groups |
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| Authors: | S Ferri TS Wu |
| Institution: | a Departamento de Matemáticas, Universidad de los Andes, Carrera 1.a 18 A 10, Bogotá, Apartado Aéreo 4976, Colombia b Departamento de Matemáticas, Universidad Jaume I, Área Científico-Técnica, 8029-AP Castellón, Spain c Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA |
| 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. |
| Keywords: | primary 22A05 54H11 secondary 54E52 |
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