Accession Number : ADA018512

Title :   Unique Reducibility of Subsets of Commutative Topological Groups and Semigroups.

Descriptive Note : Technical rept.,


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