Real Analysis Exchange

Continuity and Differentiability Aspects of Metric Preserving Functions

Robert W. Vallin

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Abstract

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.

Article information

Source
Real Anal. Exchange, Volume 25, Number 2 (1999), 849-868.

Dates
First available in Project Euclid: 3 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1230995419

Mathematical Reviews number (MathSciNet)
MR1778537

Zentralblatt MATH identifier
1016.26004

Subjects
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]

Keywords
metric spaces continuity differentiability

Citation

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


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