Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Space curves that point almost everywhere

Author: J. B. Wilker
Journal: Trans. Amer. Math. Soc. 250 (1979), 263-274
MSC: Primary 53A04
MathSciNet review: 530055
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Abstract: We construct a simple, closed, continuously differentiable curve $ r:\,[0,\,1]\, \to \,{E^d}\,(d\, \geqslant \,3)$ whose tangent vector never points twice in the same direction of $ {S^{d\, - \,1}}$ yet sweeps out a set of directions equal to almost all of $ {S^{d\, - \,1}}$.

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Keywords: Peano curve, Osgood curve, Vitali covering theorem
Article copyright: © Copyright 1979 American Mathematical Society