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What (who) is locally convex - definition
Locally convex topological vector space
TYPE OF TOPOLOGICAL VECTOR SPACE
Locally convex; Locally convex space; Locally convex spaces; Locally convex topology; Locally convex basis; Locally convex vector space; LCTVS; Finest locally convex topology
In functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can be defined as topological vector spaces whose topology is generated by translations of balanced, absorbent, convex sets.
Locally convex vector lattice
In mathematics, specifically in order theory and functional analysis, a locally convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space.
convex hull
![A [[bagplot]]. The outer shaded region is the convex hull, and the inner shaded region is the 50% Tukey depth contour.](https://commons.wikimedia.org/wiki/Special:FilePath/Bagplot.png?width=200 "A [[bagplot]]. The outer shaded region is the convex hull, and the inner shaded region is the 50% Tukey depth contour.")
![An [[oloid]], the convex hull of two circles in 3d space](https://commons.wikimedia.org/wiki/Special:FilePath/Oloid structure.svg?width=200 "An [[oloid]], the convex hull of two circles in 3d space")
![Partition of seven points into three subsets with intersecting convex hulls, guaranteed to exist for any seven points in the plane by [[Tverberg's theorem]]](https://commons.wikimedia.org/wiki/Special:FilePath/Tverberg heptagon.svg?width=200 "Partition of seven points into three subsets with intersecting convex hulls, guaranteed to exist for any seven points in the plane by [[Tverberg's theorem]]")
![The [[witch of Agnesi]]. The points on or above the red curve provide an example of a closed set whose convex hull is open (the open [[upper half-plane]]).](https://commons.wikimedia.org/wiki/Special:FilePath/Versiera007.svg?width=200 "The [[witch of Agnesi]]. The points on or above the red curve provide an example of a closed set whose convex hull is open (the open [[upper half-plane]]).")
NOTION IN TOPOLOGICAL VECTOR SPACES
Convex envelope; Closed convex hull; Convex Hull; Convex span; Convex closure; Minimum convex polygon; Applications of convex hulls
<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.
(1997-08-03)
