Über die Stetigkeit einer Funktion von zwei Veränderlichen unter Monotonie-Bedingungen - Krtscha, Manfred; Volkmann, Peter (Annales Mathematicae Silesianae, 1991)
Let T, E, F be topological spaces, and let E, F also be preordered with some compatibility between topology and order stucture. Theorem: If f(t,x): T×E→F is separately continuous with respect to its variables and monotone non-decreasing with respect to x, then f is continuous. The case of ordered normed spaces E, F is discussed in detail.