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When $C_p(X)$ is domain representable

Volume 223 / 2013

William Fleissner, Lynne Yengulalp Fundamenta Mathematicae 223 (2013), 65-81 MSC: Primary 54C30; Secondary 54B10, 54E50. DOI: 10.4064/fm223-1-5


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, $ T_2$, and $C_p(X,\mathbb {D})$ is subcompact, then $X$ is discrete.


  • William FleissnerDepartment of Mathematics
    University of Kansas
    Lawrence, KS 66045, U.S.A.
  • Lynne YengulalpDepartment of Mathematics
    University of Dayton
    Dayton, OH 45469, U.S.A.

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