On paracompactness, completeness and boundedness in uniform spaces (Q266319)

In an earlier paper [Ann. Acad. Sci. Fenn., Math. 39, No. 2, 733--758 (2014; Zbl 1303.54010)] the authors introduced two new notions of completeness in metric spaces, namely Bourbaki-completeness and cofinal Bourbaki-completeness. The goal of the present paper is to extend these investigations to general uniform spaces. In particular they study how these properties are related to conditions of uniform paracompactness and to a property called Bourbaki-boundedness. Several examples illustrate the obtained results.