Real Analysis Exchange
- Real Anal. Exchange
- Volume 25, Number 2 (1999), 849-868.
Continuity and Differentiability Aspects of Metric Preserving Functions
A function $f$ is metric preserving if for every metric space $(M,\rho)$ we have that $f \circ \rho$ is still a metric on $M$. In this article we look at the behavior of such functions with respect to continuity and differentiability. We include several pathological examples and some open questions.
Real Anal. Exchange, Volume 25, Number 2 (1999), 849-868.
First available in Project Euclid: 3 January 2009
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 54E30: Moore spaces
Secondary: 54E35: Metric spaces, metrizability 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]
Vallin, Robert W. Continuity and Differentiability Aspects of Metric Preserving Functions. Real Anal. Exchange 25 (1999), no. 2, 849--868. https://projecteuclid.org/euclid.rae/1230995419