A geometrization of Lebesgue’s space-filling curve

descriptionPublicationkeyboard_double_arrow_right Article , Part of book or chapter of book 01 Sep 1993 English Publisher:Springer Science and Business Media LLCJournal:The Mathematical Intelligencer, volume 15, pages 37-43 (issn: 0343-6993,

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Authors: Sagan, Hans;

doi: 10.1007/bf03024322 , 10.1007/978-1-4613-0195-0_17

A geometrization of Lebesgue’s space-filling curve

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Abstract

This note is a clear expository paper on space-filling curves (Osgood's curve, Lebesgue's curve, Peano's curve). Relations between different proofs are shown and some figures are provided to make easier the understanding of the limit constructions.

Related Organizations

North Carolina State University
United States
North Carolina Agricultural and Technical State University
United States

Keywords

Osgood's curve, space-filling curves, Special maps on topological spaces (open, closed, perfect, etc.), Peano's curve, Lebesgue's curve, limit of a family of curves

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