# closed convex hull

数学における凸包（とつほう、英: convex hull）または凸包絡（とつほうらく、英: convex envelope）は、与えられた集合を含む最小の凸集合である。例えば X がユークリッド平面内の有界な点集合のとき、その凸包は直観的には X をゴム膜で包んだときにゴム膜 . In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space is the . If the convex hull of X is a closed set (as happens, for instance, if X is a finite set or more generally a compact set), then it is the intersection of all closed half-spaces containing X. 2017/04/14 - Then the closure of the convex hull is the closed upper half plane { ( x , y ) : y ≥ 0 } , but the convex hull of the closure is the open upper half plane { ( x , y ) : y > 0 } . shareciteimprove this answer. answered Nov 5 '12 at 16:29. Per MannePer . Equivalently, if is the collection of all closed convex sets contains then the closed convex hull of is . The closed convex hull of some sets in are given below: Screen%20Shot%202018-03-30%20at%201.42.49%. Definition 3.4 The convex hull conv(P) of a set P ⊆ Rd is the intersection of all convex . characterizes the convex hull in terms of exactly those convex combinations that appeared (b) The convex hull of a closed subset of Rd is closed. The problem of characterizing those sets in a locally convex space X which are expressible as a closed convex hull of the range of an. X-valued measure on a o-algebra could be of interest in various contexts. It can be interpreted, for example, . Looking for Closed convex hull? Find out information about Closed convex hull. The smallest convex set containing a given collection of points in a real linear space. Also known as convex linear hull. For a set S in space, the smallest. Given a function f : ℝn → (-∞,+∞] and its closed convex hull cof, we consider the question of expressing the subdifferential of cof in terms of the subdifferential of f. Under a fairly general assumption on the behavior of f at infinity, we obtain an . 1991 Mathematics Subject Classi cation: 52A20. 1. Introduction. It is a well-known, elementary fact that the convex hull of a closed bounded set in nite-. dimensional space is closed. When is the convex hull of an unbounded (closed) set closed . the closed convex hull of a set A, denoted co A, is the smallest closed convex set including A. By Lemma 5.27(6) it is the closure of coA, that is, coA = coA. The next lemma presents further results on the relationship between topolog- ical and .