TY - JOUR
AU - Buzyakova, Raushan
PY - 2021/04/01
Y2 - 2023/12/11
TI - A glance into the anatomy of monotonic maps
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 22
IS - 1
SE -
DO - 10.4995/agt.2021.12291
UR - https://ojs.upv.es/index.php/AGT/article/view/12291
SP - 1-10
AB - <p>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.</p>
ER -