A1: LSeg |[0 ,1]|,|[1,1]| meets LSeg |[1,0 ]|,|[1,1]| by TOPREAL1:24, XBOOLE_0:def 7;
A2: LSeg |[0 ,0 ]|,|[1,0 ]| meets LSeg |[1,0 ]|,|[1,1]| by TOPREAL1:22, XBOOLE_0:def 7;
A3: LSeg |[0 ,0 ]|,|[0 ,1]| meets LSeg |[0 ,1]|,|[1,1]| by TOPREAL1:21, XBOOLE_0:def 7;
R^2-unit_square = (((LSeg |[0 ,0 ]|,|[0 ,1]|) \/ (LSeg |[0 ,1]|,|[1,1]|)) \/ (LSeg |[1,1]|,|[1,0 ]|)) \/ (LSeg |[1,0 ]|,|[0 ,0 ]|) by TOPREAL1:def 4, XBOOLE_1:4;
hence R^2-unit_square is connected by A3, A2, A1, JORDAN1:8; :: thesis: verum