Accession Number : ADA018512
Title : Unique Reducibility of Subsets of Commutative Topological Groups and Semigroups.
Descriptive Note : Technical rept.,
Corporate Author : WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS
Personal Author(s) : Klee,Victor ; Gale,David
Report Date : SEP 1975
Pagination or Media Count : 44
Abstract : As the term is used here, a reduction of a set is a direct sum decomposition into indecomposable summands. The main goal is to find conditions under which reductions are literally unique, but weaker sorts of uniqueness (akin to that of the Krull-Schmidt theorem) are also considered. The problem of unique reducibility is a classical one in many contexts, but our approach - particular, its exploitation of the key geometric notion of extreme point in conjunction with combinatorial methods involving the refinement property - appears to be new. Special cases of the main result have been obtained by Isbell in studying factorizations of Banach speaces and by Heller in studying stochastic automata.
Descriptors : *Combinatorial analysis, *Groups(Mathematics), Convex sets, Stochastic processes, Topology, Theorems, Banach space
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE