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The Koch curve as a smooth manifold

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  • Epstein, Marcelo
  • Śniatycki, Jędrzej

Abstract

We show that there exists a homeomorphism between the closed interval [0,1]⊂R and the Koch curve endowed with the subset topology of R2. We use this homeomorphism to endow the Koch curve with the structure of a smooth manifold with boundary.

Suggested Citation

  • Epstein, Marcelo & Śniatycki, Jędrzej, 2008. "The Koch curve as a smooth manifold," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 334-338.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:2:p:334-338
    DOI: 10.1016/j.chaos.2006.11.036
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    Cited by:

    1. Beardon, Alan F. & Rowat, Colin, 2013. "Efficient sets are small," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 367-374.
    2. Carpinteri, Alberto & Pugno, Nicola & Sapora, Alberto, 2009. "Asymptotic analysis of a von Koch beam," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 795-802.
    3. Chen, Zhiying & Liu, Yong & Zhou, Ping, 2018. "A comparative study of fractal dimension calculation methods for rough surface profiles," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 24-30.

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