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

William Fleissner; Lynne Yengulalp — 2013

Fundamenta Mathematicae

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 $C_{p} (X,)$ is subcompact, then X is discrete.

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Squares of Q sets

Separation properties in Moore spaces

Nonnormality points of βX∖X

When $C_{p} (X)$ is domain representable

Metrizability of certain Pixley-Roy spaces

Ultraparacompactness in certain Pixley-Roy hyperspaces

Box products of Baire spaces

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Formula preview

Currently displaying 1 – 7 of 7

Squares of Q sets

Separation properties in Moore spaces

Nonnormality points of βX∖X

When C p ( X ) is domain representable

Metrizability of certain Pixley-Roy spaces

Ultraparacompactness in certain Pixley-Roy hyperspaces

Box products of Baire spaces

When $C_{p} (X)$ is domain representable