On fiber diameters of continuous maps

Peter S. Landweber; Emanuel A. Lazar; Neel Patel

doi:10.4169/amer.math.monthly.123.4.392

On fiber diameters of continuous maps

Peter S. Landweber
, Emanuel A. Lazar
, Neel Patel

Rutgers - The State University of New Jersey, New Brunswick
University of Pennsylvania School of Arts and Sciences

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We present a surprisingly short proof that for any continuous map f: ℝⁿ → ℝ^m, if n > m, then there exists no bound on the diameter of fibers of f. Moreover, we show that when m = 1, the union of small fibers of f is bounded; when m > 1, the union of small fibers need not be bounded. Applications to data analysis are considered.

Original language	English
Pages (from-to)	392-397
Number of pages	6
Journal	American Mathematical Monthly
Volume	123
Issue number	4
DOIs	https://doi.org/10.4169/amer.math.monthly.123.4.392
State	Published - 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© THE MATHEMATICAL ASSOCIATION OF AMERICA.

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10.4169/amer.math.monthly.123.4.392

Cite this

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On fiber diameters of continuous maps

Abstract

Bibliographical note

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