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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2002 | 172 | 1 | 1-17

## A minimal regular ring extension of C(X)

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.

1-17

wydano
2002

### Twórcy

autor
• Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, U.S.A.
autor
• Department of Mathematics, Concordia University, Montreal, Québec, Canada H4B 1R6
autor
• Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2