Big Free Groups are Almost Free
arXiv:1312.4750 · doi:10.1142/S0218196715500216
Abstract
It is shown that the big free group (the set of countably-long words over a countable alphabet) is almost free, in the sense that any function from the alphabet to a compact topological group factors through a homomorphism. This statement is in fact a simple corollary of the more general result proven below on the extendability of homomorphisms from subgroups (of a certain kind) of the big free group to a compact topological group.
10 pages, several arguments expanded with no change in the results, one reference added