A shrinkability criterion for complete metric spaces

✍ Scribed by Michael Pulte; Arlo W. Schurle

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 101 KB
• Volume: 93
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00263-0

✦ Synopsis

A shrinking criterion for upper semicontinuous decompositions of a locally compact metric space is extended to complete metric spaces, answering a question of . This particular criterion thus fits into the general framework exhibited by the other results in this area (Daverman, 1986, Sections 5 and 6). This includes particularly the fundamental theorem of R.D. Edwards and L.C. , later polished by A. Marin and Y.M. which shows that shrinkability of an upper semicontinuous decomposition of a complete metric space is equivalent to the projection map being a near-homeomorphism.