The local and global 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 coincidence of these topologies on C(X,Y) is investigated for some classes of spaces: topological groups, zero-dimensional metric spaces, omega_mu-metric spaces.
Hausdorff topology and uniform convergence topology in spaces of continuous functions
ARTICO, GIULIANO;MARCONI, UMBERTO
1995
Abstract
The local and global 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 coincidence of these topologies on C(X,Y) is investigated for some classes of spaces: topological groups, zero-dimensional metric spaces, omega_mu-metric spaces.File in questo prodotto:
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