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A minimal regular ring extension of C(X)

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Henriksen M., Raphael R., Woods R.

Fundamenta Mathematicae

2002

tom 172

nr 1

1-17

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Henriksen M.

1 Raphael R.

1 Woods R.

1 2002

Wyniki wyszukiwania

A minimal regular ring extension of C(X)