Fixed points and products (Q1337567)

We say that an ordered set \(P\) has the fixed-point property if each isotone map from \(P\) to \(P\) has a fixed point. In this paper it is proved (Theorem 1.1) that the cardinal product of two finite ordered sets \(P\) and \(X\) with the fixed-point property has this property as well. In the conclusion the author remarks that this theorem was extended (by the author, B. Schröder and others) to more general situations, e.g., to the case where only one of the ordered sets \(P\) and \(X\) with the fixed- point property is finite.