# Hausdorff topology and uniform convergence topology in spaces of continuous functions

Umberto Artico; Giuliano Marconi

Commentationes Mathematicae Universitatis Carolinae (1995)

- Volume: 36, Issue: 4, page 765-773
- ISSN: 0010-2628

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topArtico, Umberto, and Marconi, Giuliano. "Hausdorff topology and uniform convergence topology in spaces of continuous functions." Commentationes Mathematicae Universitatis Carolinae 36.4 (1995): 765-773. <http://eudml.org/doc/247773>.

@article{Artico1995,

abstract = {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.},

author = {Artico, Umberto, Marconi, Giuliano},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {hyperspace; Hausdorff metric and uniformity; metric manifold; Hausdorff metric; metric manifold; Hausdorff uniformity},

language = {eng},

number = {4},

pages = {765-773},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Hausdorff topology and uniform convergence topology in spaces of continuous functions},

url = {http://eudml.org/doc/247773},

volume = {36},

year = {1995},

}

TY - JOUR

AU - Artico, Umberto

AU - Marconi, Giuliano

TI - Hausdorff topology and uniform convergence topology in spaces of continuous functions

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1995

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 36

IS - 4

SP - 765

EP - 773

AB - 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.

LA - eng

KW - hyperspace; Hausdorff metric and uniformity; metric manifold; Hausdorff metric; metric manifold; Hausdorff uniformity

UR - http://eudml.org/doc/247773

ER -

## References

top- Beer G., Metric spaces on which continuous functions are uniformly continuous and Hausdorff distance, Proc. Amer. Math. Soc. 95 (1985), 653-658. (1985) Zbl0594.54007MR0810180
- Deimling K., Nonlinear Functional Analysis, Springer-Verlag Berlin (1985). (1985) Zbl0559.47040MR0787404
- Guillemin V., Pollack A., Differential Topology, Prentice-Hall Inc. Englewood Cliffs NJ (1974). (1974) Zbl0361.57001MR0348781
- Isbell J.R., Uniform Spaces, Mathematical Surveys nr 12 AMS Providence, Rhode Island (1964). (1964) Zbl0124.15601MR0170323
- Naimpally S., Graph topology for function spaces, Trans. Amer. Math. Soc. 123 (1966), 267-272. (1966) Zbl0151.29703MR0192466

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