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A connected metric space without an equally spaced chain of points
Published online by Cambridge University Press: 17 April 2009
Abstract
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We construct a connected subspace M of the euclidean plane R2 containing two points A and B such that, for every pair of points {P, Q} of M\{A, B}, the three real numbers d(A, P), d(P, Q) and d(Q, B) are not the same. This solves a question posed by Väisälä.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 28 , Issue 2 , October 1983 , pp. 283 - 285
- Copyright
- Copyright © Australian Mathematical Society 1983
References
[1] Levy, A., Basic set theory (Springer-Verlag, Berlin, Heidelberg, New York, 1979).CrossRefGoogle Scholar
[2] Sierpinski, W., “Sur un ensemble ponctiforme connexe”, Fund. Math. 1 (1920), 7–10.CrossRefGoogle Scholar
[3] Väisälä, J., “Dividing an arc to subarcs with equal chords”, Colloq. Math. 46 (1982), 203–204.CrossRefGoogle Scholar
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