Geodesic
When $C_p(X)$ is domain representable
William Fleissner 1   ; Lynne Yengulalp 2
1 Department of Mathematics University of Kansas Lawrence, KS 66045, U.S.A.
2 Department of Mathematics University of Dayton Dayton, OH 45469, U.S.A.
Fundamenta Mathematicae, Tome 223 (2013) no. 1, pp. 65-81 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm223-1-5
Keywords: metrizable group dense subgroup prove domain representable following corollaries answer questions completely regular domain representable discrete zero dimensional mathbb subcompact discrete

William Fleissner  1   ; Lynne Yengulalp  2

1 Department of Mathematics University of Kansas Lawrence, KS 66045, U.S.A.
2 Department of Mathematics University of Dayton Dayton, OH 45469, U.S.A. 
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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

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