Ekeland's principle for vector-valued maps based on the characterization of uniform spaces via families of generalized quasi-metrics.
The purpose of this note is to prove the exponential law for uniformly continuous proper maps.
A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. We introduce and study a new cardinal invariant of a ballean, the extraresolvability, which is an asymptotic reflection of the corresponding invariant of a topological space.