Banach-stone-like theorems for lattices OF uniformly continuous functions

Abstract

New couples of uniform spaces X, Y are found out for which a lattice isomorphism between U(X) and U(Y) implies a uniform homeomorphism between X and Y.

Keywords: Banach-Stone, lattice of uniformly continuous functions, R-generated uniform space

Quaestiones Mathematicae 35(2012), 417–430