When $C_p(X)$ is domain representable

• Autorzy: William Fleissner , Lynne Yengulalp
• Języki publikacji: EN

Abstrakty

EN

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 $C_p(X,𝔻)$ is subcompact, then X is discrete.

Kategorie tematyczne

• 54B10: Product spaces
• 54C30: Real-valued functions
• 54E50: Complete metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 223
• Numer: 1
• Strony: 65-81

Daty

wydano

2013

Twórcy

autor

William Fleissner

• Department of Mathematics, University of Kansas, Lawrence, KS 66045, U.S.A.

autor

Lynne Yengulalp

• Department of Mathematics, University of Dayton, Dayton, OH 45469, U.S.A.

Identyfikatory

DOI

10.4064/fm223-1-5