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Wallman covers of compact spaces

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Henriksen M., Vermeer J., Woods R. G.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS §1. Introduction.......................................................................................................5 §2. The construction of the Wallman cover.............................................................8 §3. The minimal clopen cozero-complemented cover of a compact space............16 §4. Wallman compactifications versus Wallman cover...........................................24 References...........................................................................................................31

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A minimal regular ring extension of C(X)

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Henriksen M., Raphael R., Woods R.

Fundamenta Mathematicae

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2002

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tom 172

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nr 1

1-17

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.

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Residue class fields of lattice-ordered algebras

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Henriksen M., Isbell J. R., Johnson D. G.

Fundamenta Mathematicae

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1961-1962

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tom 50

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nr 2

107-117

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On the structure of a class of archimedean lattice-ordered algebras

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Henriksen M., Johnson D. G.

Fundamenta Mathematicae

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1961-1962

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tom 50

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nr 1

73-94

Ograniczanie wyników

3 Fundamenta Mathematicae

4 Henriksen M.

2 Johnson D. G.

1 Isbell J. R.

1 Raphael R.

1 Vermeer J.

1 Woods R.

1 Woods R. G.

1 2002

1 1989

2 1961

Wallman covers of compact spaces

A minimal regular ring extension of C(X)

Residue class fields of lattice-ordered algebras

On the structure of a class of archimedean lattice-ordered algebras