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Automatic continuity for homomorphisms into free products. (English) Zbl 1315.03084

Summary: A homomorphism from a completely metrizable topological group into a free product of groups whose image is not contained in a factor of the free product is shown to be continuous with respect to the discrete topology on the range. In particular, any completely metrizable group topology on a free product is discrete.

MSC:

03E15 Descriptive set theory
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
22A05 Structure of general topological groups
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
46H40 Automatic continuity
54H11 Topological groups (topological aspects)
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