Dieudonné completeness of a space of closed subsets and extensions of an open-closed map

✍ Scribed by Haruto Ohta

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 333 KB
• Volume: 82
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00046-1

✦ Synopsis

We prove: if X is a paracompact Hausdorff space, then the space 2x of all nonempty closed subsets of X with the Vietoris topology is DieudonnC complete. If f : X -+ Y is an open-closed continuous onto map and 2 ~4~) is DieudonnC complete, then the extension p(f) : p(X) + p(Y) is open-closed, where p(X) is the DieudonnC completion of X.