Summary.
We prove that any homeomorphism mapping a real interval onto itself and having no fixed points is conjugate to its inverse by a continuous involution or, equivalently, is a composition of two continuous decreasing involutions. As a consequence it is shown that any homeomorphism of an open interval can be represented as a composition of at most four continuous decreasing involutions.
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Received: January 28, 2000, revised version: October 16, 2000.
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Jarczyk, W. Reversibility of interval homeomorphisms without fixed points. Aequat. Math. 63, 66–75 (2002). https://doi.org/10.1007/s00010-002-8005-9
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DOI: https://doi.org/10.1007/s00010-002-8005-9