A Look at Biseparating Maps from an Algebraic Point of View

Authors

Melvin Henriksen, Harvey Mudd CollegeFollow
Frank A. Smith, Kent State UniversityFollow

Document Type

Article

Department

Mathematics (HMC)

Publication Date

2000

Abstract

In [ABN], Araujo, Beckenstein, and Narici add the capstone to a series of papers by several groups of authors by showing that if ρ is a biseparating map between two algebras of all real or complex-valued functions on realcompact spaces, then it is a continuous multiple of an isomorphism between these rings. Their proof uses relatively powerful analytic and topological techniques. In what follows, the extent to which such a result can be generalized to a wider class of algebras using algebraic techniques is investigated. We are unable, however to obtain the main result of [ABN] using these techniques.

Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,275.

Publisher pdf, posted with permission.

Rights Information

© 2000 American Mathematical Society

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Recommended Citation

Henriksen, M., and F. A. Smith. "A look at biseparating maps from an algebraic point of view." Contemporary Math 253 (2000): 135-144.