Publication

On Variations of the Convex Hull Operator

1996
Reports

Abstract

Given a collection ${\cal F}$ of subsets of $R^n$ , consider the operator $\mbox{hull}_{{\cal F}}$ associating to a set $X \subset R^n$ the intersection of all elements of ${\cal F}$ containing $X$ . The aim of this note is the study of the operator $\mbox{hull}_{{\cal F}}$ and especially its relationship with the {\em convex hull} operator in the special case when ${\cal F}$ is the set of all half-spaces of $R^n$ .

Official source

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

1996
Reports

Abstract

Official source

Related concepts (22)

Closure operator

In mathematics, a closure operator on a set S is a function from the power set of S to itself that satisfies the following conditions for all sets {| border="0" |- | | (cl is extensive), |- | | (cl is increasing), |- | | (cl is idempotent). |} Closure operators are determined by their closed sets, i.e., by the sets of the form cl(X), since the closure cl(X) of a set X is the smallest closed set containing X. Such families of "closed sets" are sometimes called closure systems or "Moore families".

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.

Convex hull

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. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact.

Related publications (3)

On Variations of the Convex Hull Operator

Chat with Graph Search

Stability and Delay Bounds in Heterogeneous Networks of Aggregate Schedulers

Dielectric Tensor Operator of Hot Plasmas in Toroidal Axisymmetrical Systems

Randomization in the two-parameter optimal stopping problem : combinatorial, probabilistic and infinitesimal methods