Abstract
A topological group G is called PR-factorizable if, for every continuous function f:G→R, one can find a perfect homomorphism p:G→H onto a second-countable topological group H and a continuous function g:H→R such that f=g∘p. We show that a topological group G is PR-factorizable if and only if G is Lindelöf feathered. We also get some other equivalent conditions for the PR-factorizability of topological groups. We show that if G is a Sánchez-Okunev complete PR-factorizable topological group, then for any continuous mapping f:G→R there exist a Polish topological group H, a perfect homomorphism g:G→H and a continuous function h:H→R such that f=h∘g. We finally show that if G is a Lindelöf feathered topological group, then G is Čech-complete if and only if G is Sánchez-Okunev complete.
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