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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


IMPACT FACTOR 2018: 0.490

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1337-2211
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Volume 66, Issue 3

Issues

A construction of a Peano curve

Egbert Harzheim
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  • Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf Universitätsstrasse 1 40225 Düsseldorf GERMANY
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Published Online: 2016-08-17 | DOI: https://doi.org/10.1515/ms-2015-0161

Abstract

PEANO, G.: Sur une courbe, qui remplit toute une aire plane, Math. Ann. 36 (1890), 157–160] invented a surjective continuous mapping f of the unit interval I = [0, 1] onto I× I. A wellknown geometric construction was given by [HILBERT, D.: Über die stetige Abbildung einer Linie auf ein Flächenstück, Math. Ann. 38 (1891), 459–460]. In general Peano curves are constructed as limit of a series of piecewise linear functions. We here present another type of proof. A detailed survey on Peano curves is given in [WUNDERLICH, W.: Über Peano-Kurven, Elem. Math. 28 (1973), 1–10].

MSC 2010: Primary 26A03, 26A30; Secondary 55M10

Key words: Peano curve

References

  • [1]

    Hilbert, D.: Über die stetige Abbildung einer Linie auf ein Flächenstück, Math. Ann. 38 (1891), 459–460.Google Scholar

  • [2]

    Peano, G.: Sur une courbe, qui remplit toute une aire plane, Math. Ann. 36 (1890), 157–160.Google Scholar

  • [3]

    Wunderlich, W.: Über Peano-Kurven, Elem. Math. 28 (1973), 1–10.Google Scholar

About the article


Received: 2012-11-12

Accepted: 2013-04-06

Published Online: 2016-08-17

Published in Print: 2016-06-01


Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 583–584, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0161.

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