Open maps on manifolds which do not admit disjoint closed subsets intersecting each fiber
✍ Scribed by Hisao Kato; Michael Levin
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 95 KB
- Volume
- 103
- Category
- Article
- ISSN
- 0166-8641
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✦ Synopsis
Let X and Y be compacta. A map f : X → Y is said to satisfy Bula's property if there exist disjoint closed subsets F 0 and
Dranishnikov constructed an open surjective map of infinite-dimensional compacta with fibers homeomorphic to a Cantor set which does not satisfy Bula's property. We construct another type of maps, namely, monotone open maps on n-manifolds, n 3 with nontrivial fibers which do not have Bula's property. Our construction essentially applies Brown's theorem (1958) on a continuous decomposition of R n \ {0} into hereditarily indecomposable continua separating between 0 and ∞. We present a relatively short proof of Brown's theorem based on the approach of Levin (1996). Related results are discussed.