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):

Report Date:

1975-09-01

Pagination or Media Count:

44.0

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.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE