Unions of Increasing and Intersections of Decreasing Sequences of Convex Sets.
Abstract
For a convex set X in a real vector space, let C(X) denote the class of all convex subsets of X, U(X) the class of all unions of strictly increasing sequences in C(X), and I(X) the class of all intersections of strictly decreasing sequences in C(X). Let U prime (X) = C(X) about = U(X) and I prime (X) = C(X) about = I(X). The purpose of the paper is to describe the subclasses U(X) and I(X) (or, equivalently, U prime (X) and I prime (X)) in geometric terms, especially when X is a finite-dimensional flat. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1972
- Accession Number
- AD0739710
Entities
People
- Victor R. Klee
Organizations
- University of Washington