Displaying similar documents to “Hit-and-far-miss Topologies”

Hausdorff topology and uniform convergence topology in spaces of continuous functions

Umberto Artico, Giuliano Marconi (1995)

Commentationes Mathematicae Universitatis Carolinae

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The local coincidence of the Hausdorff topology and the uniform convergence topology on the hyperspace consisting of closed graphs of multivalued (or continuous) functions is related to the existence of continuous functions which fail to be uniformly continuous. The problem of the local coincidence of these topologies on C ( X , Y ) is investigated for some classes of spaces: topological groups, zero-dimensional spaces, metric manifolds.

Continuity properties up to a countable partition.

Aníbal Moltó, José Orihuela, Stanimir Troyanski, Manuel Valdivia (2006)

RACSAM

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Approximation and rigidity properties in renorming constructions are characterized with some classes of simple maps. Those maps describe continuity properties up to a countable partition. The construction of such kind of maps can be done with ideas from the First Lebesgue Theorem. We present new results on the relationship between Kadec and locally uniformly rotund renormability as well as characterizations of the last one with the simple maps used here.