A minimal regular ring extension of C(X)

• Autorzy: M. Henriksen , R. Raphael , R. G. Woods
• Języki publikacji: EN

Abstrakty

EN

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 $τ ⊆ τ_δ$ 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.

Kategorie tematyczne

• 54G10: P -spaces
• 46E25: Rings and algebras of continuous, differentiable or analytic functions
• 16E50: von Neumann regular rings and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 172
• Numer: 1
• Strony: 1-17

Daty

wydano

2002

Twórcy

autor

M. Henriksen

• Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, U.S.A.

autor

R. Raphael

• Department of Mathematics, Concordia University, Montreal, Québec, Canada H4B 1R6

autor

R. G. Woods

• Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

Identyfikatory

DOI

10.4064/fm172-1-1