Uniform continuity for all distance spaces

In this paper, we present a definition of uniform continuity which applies to morphisms in the category DST of distance spaces, and which generalizes the definitions of uniform continuity which apply in the categories of metric spaces, of nearness spaces and of zeroed distance spaces. This definition allows us to define a category BDUNIF, of d-bounded distance spaces and uniformly continuous functions (with this new definition of uniform continuity). TOP is embedded in BDUNIF as a bi-coreflective subcategory.