Real Analysis Exchange

A characterization of rings of density continuous functions.

Michelle L. Knox

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Abstract

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.

Article information

Source
Real Anal. Exchange, Volume 31, Number 1 (2005), 165-178.

Dates
First available in Project Euclid: 5 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149516804

Mathematical Reviews number (MathSciNet)
MR2218196

Zentralblatt MATH identifier
1097.54019

Subjects
Primary: 54C30: Real-valued functions [See also 26-XX]
Secondary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}

Keywords
Density topology density continuous function $P$-space

Citation

Knox, Michelle L. A characterization of rings of density continuous functions. Real Anal. Exchange 31 (2005), no. 1, 165--178. https://projecteuclid.org/euclid.rae/1149516804


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References

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