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

Slutsky, Konstantin

J. Symb. Log. 78, No. 4, 1288-1306 (2013).

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)