Ordered spaces and quasi-uniformities on spaces of continuous order-preserving functions (Q2721516)

The author obtains versions of well-known and fundamental topological results about function spaces (equipped with the point-open resp. compact-open topology) in the setting of ordered topological spaces. For instance the classical result that for spaces of continuous functions the topology of compact convergence is the compact-open topology is generalized in an appropriate way to the category of ordered topological spaces and order-preserving continuous maps. NEWLINENEWLINENEWLINEFrom a categorical point of view he also compares his results with related results of bitopological nature due to \textit{S. Romaguera} and \textit{M. Ruiz-Gómez} [Publ. Math. 47, No. 1-2, 81-93 (1995; Zbl 0851.54030) and 50, No. 1-2, 1-15 (1997; Zbl 0909.54027)]. Finally, he establishes that the property of strict complete (order) regularity (in the sense of J.D. Lawson) is transferred from the codomain to the introduced ordered topological function spaces.