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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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