Relations approximated by continuous functions

Authors:
L'. Holá and R. A. McCoy

Journal:
Proc. Amer. Math. Soc. **133** (2005), 2173-2182

MSC (2000):
Primary 54C35, 54B20, 54C08

DOI:
https://doi.org/10.1090/S0002-9939-05-07793-2

Published electronically:
February 15, 2005

MathSciNet review:
2137885

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Tychonoff space, let be the space of all continuous real-valued functions defined on and let be the hyperspace of all nonempty closed subsets of . We prove the following result. Let be a locally connected, countably paracompact, normal -space without isolated points, and let . Then is in the closure of in with the locally finite topology if and only if is the graph of a cusco map. Some results concerning an approximation in the Vietoris topology are also given.

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Additional Information

**L'. Holá**

Affiliation:
Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia

Email:
hola@mat.savba.sk

**R. A. McCoy**

Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

Email:
mccoy@math.vt.edu

DOI:
https://doi.org/10.1090/S0002-9939-05-07793-2

Keywords:
Set-valued mapping,
Vietoris topology,
locally finite topology,
upper-semicontinuous multifunction,
usco map,
cusco map

Received by editor(s):
October 14, 2003

Received by editor(s) in revised form:
April 8, 2004

Published electronically:
February 15, 2005

Communicated by:
Alan Dow

Article copyright:
© Copyright 2005
American Mathematical Society