let P be Subset of (TOP-REAL 2); :: thesis: ( P is being_S-P_arc implies ex f being Function of I[01],((TOP-REAL 2) | P) st f is being_homeomorphism )
assume P is being_S-P_arc ; :: thesis: ex f being Function of I[01],((TOP-REAL 2) | P) st f is being_homeomorphism
then consider p1, p2 being Point of (TOP-REAL 2) such that
A1: P is_an_arc_of p1,p2 by Th28;
ex f being Function of I[01],((TOP-REAL 2) | P) st
( f is being_homeomorphism & f . 0 = p1 & f . 1 = p2 ) by A1;
hence ex f being Function of I[01],((TOP-REAL 2) | P) st f is being_homeomorphism ; :: thesis: verum