Resumen de Reversibility of interval homeomorphisms without fixed points

Witold Jarczyk

• 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.