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b-uniform filter spaces are an appropriate tool for studying convergence from a higher point of view as demonstrated in two papers by the above mentioned authors. Fundamental properties of spaces in topology such as completeness, precompactness or compactness, respectively, can be newly defined and studied in the realm of these proper constructs. Moreover, we present a kind of completion, called Cauchy completion, which generalizes the corresponding concepts that arose in the past like the simple completion of semi-uniform convergence spaces in the sense of [10], the Wyler completion of separated uniform limit spaces [15], the Hausdorff completion of separated uniform spaces or the λ-completion of filter spaces in the sense of [2], and, last not least, the compactification of proximity spaces ([4], or [12], respectively). [ABSTRACT FROM AUTHOR]

In this paper a systematic study begins of the category b-UFIL of b-uniform filter spaces and b-uniformly continuous mappings. We will show that this construct forms a quasitopos in which quotients are stable under products. Consequently, it is extremely useful for further studies in the realm of Bounded topology. [ABSTRACT FROM AUTHOR]