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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Shrinking certain sliced decompositions of $ E\sp{n+1}$


Authors: Robert J. Daverman and D. Kriss Preston
Journal: Proc. Amer. Math. Soc. 79 (1980), 477-483
MSC: Primary 54B15; Secondary 54B10
MathSciNet review: 567997
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Abstract: We set forth a connection, based on relatively elementary techniques, between the shrinkability of product decompositions of $ {E^{n + 1}}$ and that of sliced decompositions. In particular, if G is a decomposition of $ {E^{n + 1}}$ such that each decomposition element g is contained in some horizontal slice $ {E^n} \times \{ s\} $ and if the decomposition $ {G^s}$ of $ {E^n}$, consisting of those subsets g of $ {E^n}$ for which $ g \times \{ s\} \in G$ , expands to a shrinkable decomposition $ {G^s} \times {E^1}$ of $ {E^n} \times {E^1}$, we show then that G itself is shrinkable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0567997-8
PII: S 0002-9939(1980)0567997-8
Keywords: Upper semicontinuous decomposition, cell-like, shrinkable decomposition, shrinkability criterion, sliced decomposition, embedding dimension
Article copyright: © Copyright 1980 American Mathematical Society