# convex hull

(redirected from Convex closure)

## convex hull

[′kän‚veks ′həl]
(mathematics)
The smallest convex set containing a given collection of points in a real linear space. Also known as convex linear hull.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## convex hull

(mathematics, graphics)
For a set S in space, the smallest convex set containing S. In the plane, the convex hull can be visualized as the shape assumed by a rubber band that has been stretched around the set S and released to conform as closely as possible to S.
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For any X [subset] P the intersection of all convex subspaces containing X is said to be the convex closure of X.
By [8], the convex closure of every apartment of [G.sub.k]([PI]) coincides with [G.sub.k]([PI]); moreover, if A is an apartment in a parabolic subspace then the convex closure of A coincides with this parabolic subspace.
The subspace S contains the convex closure of f(A), i.e.
This follows from Proposition 3.1 and the fact that every polar space is the convex closure of any frame.
The convex closure of a nonempty set S is the least (with respect to [subset or equal to] convex set that contains S.
Now, [[union].sub.i.[Sigma].I] [down arrow] {[C.sub.i]} is downward closed and therefore convex, so the convex closure {[C.sub.i] : i [element of] I} is also contained in that set.
Because [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is downward closed, and therefore convex, and because taking convex closure only adds elements to a set, the set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] satisfies the same properties, so
Hence our convex closure [Mathematical Expression Omitted] will in general be a smaller set of worlds than the 'convex hull' of X according to Oddie.
Note that every non-degenerate polar space is the convex closure of any two of its points at distance 2 from each other.
Now (x, y) is called a special pair, the convex closure of {x, y} is the set of points on the two lines xy and yz, which is not a symp.
Note that S has diameter 2 and is the convex closure, in S, of any two points at distance 2 in S.

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