Let X be an arbitrary set. Then a topology t on X is completely useful if every upper
semicontinuous linear preorder on X can be represented by an upper semicontinuous order …

We present some lifting theorems for continuous order-preserving functions on locally and σ-
compact Hausdorff preordered topological spaces. In particular, we show that a preorder on …

We investigate properties of strongly useful topologies, ie, topologies with respect to which
every weakly continuous preorder admits a continuous order-preserving function. In …

Let X be an arbitrary set. Then a topology t on X is said to be completely useful if every upper
semicontinuous linear (total) preorder≾ on X can be represented by an upper …