let C be compact Subset of (TOP-REAL 2); :: thesis: (south_halfline (LMP C)) \ {(LMP C)} c= UBD C
set A = (south_halfline (LMP C)) \ {(LMP C)};
reconsider A = (south_halfline (LMP C)) \ {(LMP C)} as non bounded Subset of (TOP-REAL 2) by JORDAN2C:123, TOPREAL6:90;
A is convex by JORDAN21:7;
hence (south_halfline (LMP C)) \ {(LMP C)} c= UBD C by Th11, JORDAN2C:125; :: thesis: verum