let C be compact Subset of (TOP-REAL 2); :: thesis: (north_halfline (UMP C)) \ {(UMP C)} c= UBD C
set A = (north_halfline (UMP C)) \ {(UMP C)};
reconsider A = (north_halfline (UMP C)) \ {(UMP C)} as non bounded Subset of (TOP-REAL 2) by JORDAN2C:122, TOPREAL6:90;
A is convex by JORDAN21:6;
hence (north_halfline (UMP C)) \ {(UMP C)} c= UBD C by Th10, JORDAN2C:125; :: thesis: verum