ArticleOriginal scientific text
Title
Structure spaces for rings of continuous functions with applications to realcompactifications
Authors 1, 2
Affiliations
- Department of Mathematics, The Pennsylvania State University, Abington, Pennsylvania 19001, U.S.A.
- Department of Mathematics, California State University, Long Beach, California 90840, U.S.A.
Abstract
Let X be a completely regular space and let A(X) be a ring of continuous real-valued functions on X which is closed under local bounded inversion. We show that the structure space of A(X) is homeomorphic to a quotient of the Stone-Čech compactification of X. We use this result to show that any realcompactification of X is homeomorphic to a subspace of the structure space of some ring of continuous functions A(X).
Keywords
ring of continuous functions, maximal ideal, ultrafilter, realcompactification
Bibliography
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Pages:
151-163
Main language of publication
English
Received
1996-03-07
Accepted
1996-08-20
Published
1997
Exact and natural sciences