Abstract
The following result is proved: Let X X and Y Y be compact topological groups and p p be a continuous group homomorphism from Y Y onto X X . Then there exists a map q q from X X to Y Y such that p ∘ q = i d X p \circ q = {\text {i}}{{\text {d}}_X} and q − 1 ( B ) {q^{ - 1}}(B) is a Baire set in Y Y for every Baire subset B B of X X .
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