Convergence preserving mappings on topological groups |
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Authors: | Walden Freedman |
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Institution: | Department of Mathematics, Humboldt State University, 1 Harpst St, Arcata, CA 95521, USA |
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Abstract: | It is well known that a mapping is convergence preserving, that is, whenever an infinite series ∑an converges, the series ∑φ(an) converges, if and only if there exists m∈R such that φ(x)=mx in some neighborhood of 0. We explore convergence preserving mappings on Hausdorff topological groups, showing in particular, that if G×G is a Fréchet group, and H has no small subgroups, then a mapping is convergence preserving if and only if there is a neighborhood of the identity in G on which φ is a sequentially continuous homomorphism. |
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Keywords: | primary 22A05 secondary 22A10 54D55 54A20 |
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