Abstract
In this paper it is provided an explicit embedding for complete metric spaces having a star-finite base of its uniformity into the universal space kappa ^{omega _0} times mathbb {R}^{omega _0}, where kappa ge omega _0 is the cellularity of the space and kappa ^{omega _0} is the Baire space of weight kappa . From this result, similar embeddings for general Bourbaki-complete uniform spaces as well as for metric spaces are derived. In particular, these embeddings partially preserve the uniform structure of the original space. Several examples of Bourbaki-complete metric spaces having no star-finite base for its metric uniformity are constructed.
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