On compact topologies on the semigroup of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set - Gutik, O.; Shchypel, M. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 512.536 We study the topologization of the semigroup O\!\!I\!_n(L) of finite partial order isomorphisms of bounded rank of an infinite linear ordered set (L,). In particular, we show that every T_1 left-topological (right-topological) semigroup O\!\!I\!_n(L) is an Urysohn, functionally Hausdorff, totally disconnected, and scattered space. It is proved that, on the semigroup O\!\!I\!_n(L), there exists a unique Hausdorff countably compact (pseudocompact) shift-continuous topology, which is compact, and that the Bohr compactification of the Hausdorff topological semigroup O\!\!I\!_n(L) is the trivial semigroup.