Relations approximated by continuous functions |
| |
| Authors: | L'. Holá R. A. McCoy |
| |
| Affiliation: | Mathematical Institute, Slovak Academy of Sciences, Stefánikova 49, 814 73 Bratislava, Slovakia ; Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 |
| |
| 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. |
| |
| Keywords: | Set-valued mapping Vietoris topology locally finite topology upper-semicontinuous multifunction usco map cusco map |
|
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 |
|
点击此处可从《Proceedings of the American Mathematical Society》下载全文 |
|
