Vol. 53, No. 2, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
Other MSP Journals
Functional representation of algebraic intervals

Robert Edward Jamison, II

Vol. 53 (1974), No. 2, 399–423

Motivated by some examples from the study of axiomatic convexity, we define a class of objects (in real algebras with 1) whose algebraic properties mimic those of the unit interval. These objects, called intervals, have quite a bit of structure in themselves. In particular, in a Banach algebra a compact interval must be finite dimensional. Even more striking is the main result which shows that any interval satisfying a very modest boundedness condition is commutative and can be represented by continuous functions from a compact Hausdorff space into the unit interval. This leads to a number of corollaries in analysis and topology.

Mathematical Subject Classification 2000
Primary: 46H05
Secondary: 46E15
Received: 5 July 1972
Revised: 28 January 1974
Published: 1 August 1974
Robert Edward Jamison, II