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Abstract. In this paper we extend the theory of strong uniform continuity and strong uniform convergence, developed in the setting of metric spaces in [13,14], to the uniform space setting, where again the notion of shields plays a key role. Further, we display appropriate bornological/variational modifications of classical properties of Alexandroff [1] and of Bartle [7] for nets of continuous functions, that combined with pointwise convergence, yield continuity of the limit for functions between metric spaces.2000 AMS Classification: Primary 40A30, 54C35; Secondary 54E15, 54C08

In many everyday situations, we need to rank individuals or single items having the possibility to observe the behavior of groups. In this paper we propose a way to get this ranking over the elements of a set X , starting from an arbitrary preference relation over the subsets of X and taking into account the information provided by this ranking over the subsets. To this purpose, we use a very common approach in the social choice framework: we single out some properties that a general solution should satisfy, and we prove that these properties characterize a unique solution. Given the generality of the approach, we believe that this paper is only a starting point for a more extended analysis. In particular, it is clear that different contexts can suggest other properties, thus identifying alternative ranking methods.

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