Conical hull Conical combination

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in plane, conical hull of circle passing through origin open half-plane defined tangent line circle @ origin plus origin.


therefore, conical combination , conical hull more accurately called convex conical combination , convex conical hull respectively. moreover, above remark dividing coefficients while discarding origin implies conical combinations , hulls may considered convex combinations , convex hulls in projective space.


while convex hull of compact set compact set well, not conical hull: first of all, latter 1 unbounded. moreover, not closed set: counterexample sphere passing through origin, conical hull being open half-space plus origin. however, if s nonempty compact set not contain origin, conical hull of s closed set.








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