Countable Products of Čech-scattered supercomplete spaces

We prove by using well-founded trees that a countable product of supercomplete spaces, scattered with respect to ech-complete subsets, is supercomplete. This result extends results given in [1], [5], [6], [19], [26] and its proof improves that given in [19].     

On a combinatorial property of choice functions of finite sets

We consider choice functions k[X]→X, where X is a finite set and k[X] denotes the set of all k-subsets of X. We define a property of domination for such maps generalizing the classical case k=2 (tournaments) and prove the existence of a dominating element generalizing the existence of a 2-root (king) in the classical case.