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Nonnormality points of βX∖X

William Fleissner;  Lynne Yengulalp — 2011

Fundamenta Mathematicae

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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