theorem Th3: :: TOPREAL2:3

for q1, q2 being Point of (TOP-REAL 2)
for Q, P being non empty Subset of (TOP-REAL 2)
for f being Function of ((TOP-REAL 2) | Q),((TOP-REAL 2) | P) st f is being_homeomorphism & Q is_an_arc_of q1,q2 holds
for p1, p2 being Point of (TOP-REAL 2) st p1 = f . q1 & p2 = f . q2 holds
P is_an_arc_of p1,p2