On the shrinkability of decompositions of manifolds
Author:
William L. Voxman
Journal:
Trans. Amer. Math. Soc. 150 (1970), 2739
MSC:
Primary 54.78
MathSciNet review:
0261577
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Abstract: An upper semicontinuous decomposition of a metric space is said to be shrinkable in case for each covering of the union of the nondegenerate elements, for each , and for an arbitrary homeomorphism from onto , there exists a homeomorphism from onto itself such that (1) if , then , (2) for each , (a) and (b) there exists such that . Our main result is that if is a cellular decomposition of a manifold , then if and only if is shrinkable. We also define concepts of local and weak shrinkability, and we show the equivalence of the various types of shrinkability for certain cellular decompositions. Some applications of these notions are given, and extensions of theorems of Bing and Price are proved.
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 , Concerning cellular decompositions of manifolds that yield manifolds, Trans. Amer. Math. Soc. 133 (1968), 307332. MR 37 #5859. MR 0230296 (37:5859)
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 , Upper semicontinuous decompositions of , Ann. of Math. (2) 65 (1957), 363374. MR 19, 1187. MR 0092960 (19:1187f)
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 , Pointlike decompositions of , Fund. Math. 50 (1961/62), 431453. MR 25 #560. MR 0137104 (25:560)
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 K. W. Kwun, Upper semicontinuous decompositions of the sphere, Proc. Amer. Math. Soc. 13 (1962), 284290. MR 25 #3512. MR 0140089 (25:3512)
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DOI:
http://dx.doi.org/10.1090/S00029947197002615778
PII:
S 00029947(1970)02615778
Keywords:
Cellular decompositions of manifolds,
shrinkability,
0dimensional decompositions,
weakly shrinkable,
locally shrinkable
Article copyright:
© Copyright 1970
American Mathematical Society
