A Minimal Regular Ring Extension of C(X)

Authors

Melvin Henriksen, Harvey Mudd CollegeFollow
Robert M. Raphael, Concordia University
R. G. Woods, University of Manitoba

Document Type

Article

Department

Mathematics (HMC)

Publication Date

2002

Abstract

Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,Τ). We investigate when G(X) coincides with the ring C(X,Τ_δ) of continuous real-valued functions on the space (X,Τ_δ), where Τ_δ is the smallest Tikhonov topology on X for which tau subset of or equal to tau(delta) and C(X,Τ_δ) is von Neumann regular. The compact and metric spaces for which G(X) = C(X,Τ_δ) are characterized. Necessary, and different sufficient, conditions for the equality to hold more generally are found.

Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,426

Rights Information

© 2002 Institute of Mathematics, Polish Academy of Sciences

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Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Henriksen, M., R. Raphael, and R. G. Woods. "A minimal regular ring extension of C(X)." Fundamenta Mathematicae 172.1 (2002): 1-17.