Accession Number : AD0739710

Title :   Unions of Increasing and Intersections of Decreasing Sequences of Convex Sets.

Descriptive Note : Technical rept.,

Corporate Author : WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS

Personal Author(s) : Klee,Victor R.

Report Date : JAN 1972

Pagination or Media Count : 16

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)

Descriptors :   (*CONVEX SETS, THEOREMS), SEQUENCES(MATHEMATICS), VECTOR SPACES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE