In this paper,we define a new class of Pm-factorizable topological groups.A topo-logical group G is called Pm-factorizable if,for every continuous function f:G → M to a metrizable space M,one can find a perfect homomorphism π:G → K onto a second-countable topological group K and a continuous function g:K → M such that f=goπ.We show that a topological group G is Pm-factorizable if and only if it is PR-factorizable.And we get that if G is a Pm-factorizable topological group and K is any compact topological group,then the group G × K is Pm-factorizable.
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