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2005-2006 A characterization of rings of density continuous functions.
Michelle L. Knox
Author Affiliations +
Real Anal. Exchange 31(1): 165-178 (2005-2006).


A density continuous function is defined as a continuous function from a Tychonoff space $X$ into the real numbers with the density topology. The collection of density continuous functions on $X$ is denoted by $C(X,\mathbb{R}_d)$. It is shown that $C(X,\mathbb{R}_d)$ is a ring precisely when each density continuous function is locally constant, and in this case $X$ is defined to be a density $P$-space. Examples of density $P$-spaces are given.


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Michelle L. Knox. "A characterization of rings of density continuous functions.." Real Anal. Exchange 31 (1) 165 - 178, 2005-2006.


Published: 2005-2006
First available in Project Euclid: 5 June 2006

zbMATH: 1097.54019
MathSciNet: MR2218196

Primary: ‎54C30
Secondary: 26A15

Keywords: $p$-space , density continuous function , density topology

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 1 • 2005-2006
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