The Concept of State and the Axiom of Choice

✍ Scribed by Paolo d'Alessandro

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 1014 KB
• Volume: 304
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(77)90059-x

✦ Synopsis

The first part of the paper is concerned with the problem of existence of state space representations of general systems. It is shown that the axiom of choice makes possible the direct construction of a reduced state space representation of a general system under no restrictive hypotheses. Moreover, the corresponding stare spaces are shown to be, loosely speaking, the largest of all reduced state spaces. Then topological properties of state space representations are investigated for both their mathematical and system theoretic interest. 7'he properties of the previously introduced state space representation along with a function space approach are exploited to derive from standard general topology conditions for continuity of state space representations and for state space compactness. Many of the results of the ensuing theory present some new features with respect to their general topology antecedents.