for Y being non empty TopSpace
for F being Function of [:Y,I[01]:],(Tunit_circle 2)
for Ft being Function of [:Y,(Sspace 0[01]):],R^1 st F is continuous & Ft is continuous & F | [: the carrier of Y,{0}:] = CircleMap * Ft holds
ex G being Function of [:Y,I[01]:],R^1 st
( G is continuous & F = CircleMap * G & G | [: the carrier of Y,{0}:] = Ft & ( for H being Function of [:Y,I[01]:],R^1 st H is continuous & F = CircleMap * H & H | [: the carrier of Y,{0}:] = Ft holds
G = H ) )