Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Products of decompositions of $ E\sp{n}$

Author: Brian J. Smith
Journal: Trans. Amer. Math. Soc. 184 (1973), 31-41
MSC: Primary 57A15
MathSciNet review: 0328946
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Abstract: In this paper we give a sufficient condition for the existence of a homeomorphism $ h:{E^m}/G \times {E^n}/H \to {E^{m + n}}$, where G and H are u.s.c. decompositions of Euclidean space. This condition is then shown to hold for a wide class of examples in which the decomposition spaces $ {E^m}/G$ and $ {E^n}/H$ may fail to be Euclidean.

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Keywords: Upper-semicontinuous decomposition, non-Euclidean decompositions, shrinkable collections
Article copyright: © Copyright 1973 American Mathematical Society