Unique Reducibility of Subsets of Commutative Topological Groups and Semigroups.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1975
- Accession Number
- ADA018512
Entities
People
- David Gale
- Victor Klee
Organizations
- University of Washington