let C be compact Subset of ; :: 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 by JORDAN2C:131, TOPREAL6:99;
A is convex by JORDAN21:7;
hence (south_halfline (LMP C)) \ {(LMP C)} c= UBD C by Th11, JORDAN2C:133; :: thesis: verum