Buzyakova, Raushan2021-04-162021-04-162021-04-011576-9402https://riunet.upv.es/handle/10251/165234[EN] Given an autohomeomorphism on an ordered topological space or its subspace, we show that it is sometimes possible to introduce a new topology-compatible order on that space so that the same map is monotonic with respect to the new ordering. We note that the existence of such a re-ordering for a given map is equivalent to the map being conjugate (topologically equivalent) to a monotonic map on some homeomorphic ordered space. We observe that the latter cannot always be chosen to be order-isomorphic to the original space. Also, we identify other routes that may lead to similar affirmative statements for other classes of spaces and maps.Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)Monotonic mapOrdered topological spacesTopologically equivalent mapsA glance into the anatomy of monotonic mapsArtÃculo10.4995/agt.2021.12291Abierto1989-4147