theorem Th45: :: JGRAPH_1:46

for X, Y being non empty TopSpace
for f being Function of X,Y
for P being non empty Subset of Y st X is compact & Y is T_2 & f is continuous & f is one-to-one & P = rng f holds
ex f1 being Function of X,(Y | P) st
( f = f1 & f1 is being_homeomorphism )