Hausdorff topology and uniform convergence topology in spaces of continuous functions

Umberto Artico; Giuliano Marconi

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Hit-and-far-miss Topologies

Giuseppe Di Maio, Somashekhar Naimpally (2008)

Matematički Vesnik

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Cofinal completeness of the Hausdorff metric topology

Gerald Beer, Giuseppe Di Maio (2010)

Fundamenta Mathematicae

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A net in a Hausdorff uniform space is called cofinally Cauchy if for each entourage, there exists a cofinal (rather than residual) set of indices whose corresponding terms are pairwise within the entourage. In a metric space equipped with the associated metric uniformity, if each cofinally Cauchy sequence has a cluster point, then so does each cofinally Cauchy net, and the space is called cofinally complete. Here we give necessary and sufficient conditions for the nonempty closed subsets...