A glance into the anatomy of monotonic maps

<p>Given an autohomeomorphism on ordered topological space or its subspace, we show that it is sometimes possible to introduce a new topology-compatible order so the same map monotonic with respect ordering. We note existence of such re-ordering for given equivalent being conjugate (topologically equivalent) some homeomorphic space. observe latter cannot always be chosen order-isomorphic original Also, identify other routes may lead similar affirmative statements classes spaces and maps.</p>