Abstract
The purpose of this paper is first to show that if X is any locally compact but not compact perfect Polish space and Open image in new window stands for the one-point compactification of X, while EX is the equivalence relation which is defined on the Polish group C(X,R+*) by Open image in new window where f, g are in C(X,R+*), then EX is induced by a turbulent Polish group action. Second we show that given any Open image in new window if we identify the n-dimensional unit sphere Sn with the one-point compactification of Rn via the stereographic projection, while En,r is the equivalence relation which is defined on the Polish group Cr(Rn,R+*) by Open image in new window where f, g are in Cr(Rn,R+*), then En,r is also induced by a turbulent Polish group action.
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