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.
@article{10_4064_fm223_1_5,
author = {William Fleissner and Lynne Yengulalp},
title = {When $C_p(X)$ is domain representable},
journal = {Fundamenta Mathematicae},
pages = {65--81},
year = {2013},
volume = {223},
number = {1},
doi = {10.4064/fm223-1-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm223-1-5/}
}
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AU - Lynne Yengulalp
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William Fleissner; Lynne Yengulalp. When $C_p(X)$ is domain representable. Fundamenta Mathematicae, Tome 223 (2013) no. 1, pp. 65-81. doi: 10.4064/fm223-1-5
