On free vector balleans

Abstract

A vector balleans is a vector space over R en- dowed with a coarse structure in such a way that the vector opera- tions are coarse mappings. We prove that, for every ballean (X, E),

there exists the unique free vector ballean V(X, E) and describe the coarse structure of V(X, E). It is shown that normality of V(X, E) is equivalent to metrizability of (X, E).