Topological convergence and uniform convergence
Clusters and ultrafilters.
On almost complete and almost precompact quasi-uniform spaces
-proximity spaces
Hit-and-far-miss Topologies
Common fixed points for nonexpansive and asymptotically nonexpansive mappings
Normal Vietoris implies compactness: a short proof
One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.
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