locally strongly convex - определение. Что такое locally strongly convex
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  1. Словари
  2. Английский словарь
  3. locally strongly convex

Что (кто) такое locally strongly convex - определение

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

Locally convex topological vector space         
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.
https://en.wikipedia.org/wiki/Locally_convex_topological_vector_space
convex hull         
  • A [[bagplot]]. The outer shaded region is the convex hull, and the inner shaded region is the 50% Tukey depth contour.
  • Convex hull of a bounded planar set: rubber band analogy
  • Convex hull of points in the plane
  • Convex hull ( in blue and yellow) of a simple polygon (in blue)
  • 2019}} Mg<sub>2</sub>C<sub>3</sub> is expected to be unstable as it lies above the lower hull.
  • 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]]
  • 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)
Convex hull         
  • A [[bagplot]]. The outer shaded region is the convex hull, and the inner shaded region is the 50% Tukey depth contour.
  • Convex hull of a bounded planar set: rubber band analogy
  • Convex hull of points in the plane
  • Convex hull ( in blue and yellow) of a simple polygon (in blue)
  • 2019}} Mg<sub>2</sub>C<sub>3</sub> is expected to be unstable as it lies above the lower hull.
  • 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]]
  • 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
In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset.
https://en.wikipedia.org/wiki/Convex_hull

Википедия

Locally convex topological vector space

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. Alternatively they can be defined as a vector space with a family of seminorms, and a topology can be defined in terms of that family. Although in general such spaces are not necessarily normable, the existence of a convex local base for the zero vector is strong enough for the Hahn–Banach theorem to hold, yielding a sufficiently rich theory of continuous linear functionals.

Fréchet spaces are locally convex spaces that are completely metrizable (with a choice of complete metric). They are generalizations of Banach spaces, which are complete vector spaces with respect to a metric generated by a norm.

https://en.wikipedia.org/wiki/Locally convex topological vector space
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