let P be Subset of (TOP-REAL 2); :: thesis: ( P is being_simple_closed_curve implies P is connected )
given f being Function of ((TOP-REAL 2) | R^2-unit_square),((TOP-REAL 2) | P) such that A1: f is being_homeomorphism ; :: according to TOPREAL2:def 1 :: thesis: P is connected
A2: (TOP-REAL 2) | R^2-unit_square,(TOP-REAL 2) | P are_homeomorphic by A1;
(TOP-REAL 2) | R^2-unit_square is connected by CONNSP_1:def 3;
then (TOP-REAL 2) | P is connected by A2, Th17;
hence P is connected ; :: thesis: verum