Abstract
In this paper, we define a new class of PM-factorizable topological groups. A topological group G is called PM-factorizable if, for every continuous real-valued function f on G, one can find a perfect homomorphism p:G→L onto a metrizable topological group L and a continuous real-valued function h on L such that f=h∘p. The relations between PR-factorizable, PM-factorizable and M-factorizable topological groups are studied. Also, some new characterizations of PR-factorizable, PM-factorizable and M-factorizable topological groups are obtained.
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