Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4661287 | Topology and its Applications | 2007 | 8 Pages |
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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Physical Sciences and Engineering
Mathematics
Geometry and Topology