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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The mountain climbers' problem


Author: Tamás Keleti
Journal: Proc. Amer. Math. Soc. 117 (1993), 89-97
MSC: Primary 26A12; Secondary 26A15, 26A48
MathSciNet review: 1123655
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Abstract: We show that two climbers can climb a mountain in such a way that at each moment they are at the same height above the sea level, supposing that the mountain has no plateau. That is, if $ f$ and $ g$ are continuous functions mapping $ [0,1]$ to $ [0,1]$ with $ f(0) = g(0) = 0$ and $ f(1) = g(1) = 1$, and if neither $ f$ nor $ g$ has an interval of constancy then there exist continuous functions $ k$ and $ h:[0,1] \to [0,1]$ satisfying $ k(0) = h(0) = 0,\;k(1) = h(1) = 1$, and $ f \circ k = g \circ h$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1123655-1
PII: S 0002-9939(1993)1123655-1
Article copyright: © Copyright 1993 American Mathematical Society