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Nonnormality points of βX∖X

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Fleissner W., Yengulalp L.

Fundamenta Mathematicae

2011

tom 214

nr 3

269-283

Let X be a crowded metric space of weight κ that is either $κ^{ω}$-like or locally compact. Let y ∈ βX∖X and assume GCH. Then a space of nonuniform ultrafilters embeds as a closed subspace of (βX∖X)∖{y} with y as the unique limit point. If, in addition, y is a regular z-ultrafilter, then the space of nonuniform ultrafilters is not normal, and hence (βX∖X)∖{y} is not normal.

When $C_p(X)$ is domain representable

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Fleissner W., Yengulalp L.

Fundamenta Mathematicae

2013

tom 223

nr 1

65-81

Let M be a metrizable group. Let G be a dense subgroup of $M^X$. We prove that if G is domain representable, then $G = M^X$. The following corollaries answer open questions. If X is completely regular and $C_p(X)$ is domain representable, then X is discrete. If X is zero-dimensional, T₂, and $C_p(X,𝔻)$ is subcompact, then X is discrete.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Fleissner W.

2 Yengulalp L.

1 2013

1 2011

Wyniki wyszukiwania

Nonnormality points of βX∖X

When $C_p(X)$ is domain representable