The Cauchy completion of a symmetric b-uniform filter space
Abstract
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).
Keywords
symmetric b-uniform filter space, b-filter space, completeness, Cauchy completion, strong topological universe, Bounded topology, set-convergence, separation propertyPersistent identifier
http://hdl.handle.net/11012/203931Document type
Peer reviewedDocument version
Final PDFSource
Mathematics for Applications. 2021 vol. 10, č. 2, s. 125-142. ISSN 1805-3629http://ma.fme.vutbr.cz/archiv/10_2/ma_10_2_leseberg_vaziry_final.pdf
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