Summary
Given a quasi-uniform space (X,U), we study its Hausdorff quasi-uniformity UH on the set P0(X) of nonempty subsets of the set X. In particular we are concerned with the question whether at a certain finite stage iterations of the described Hausdorff hyperspace construction applied to two distinct quasi-uniformities on X will necessarily lead to hyperspaces carrying distinct induced topologies.
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Künzi, HP. Iterations of quasi-uniform hyperspace constructions. Acta Math Hung 113, 213–225 (2006). https://doi.org/10.1007/s10474-006-0100-2
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DOI: https://doi.org/10.1007/s10474-006-0100-2