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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A general class of factors of $ E^4$


Author: Leonard R. Rubin
Journal: Trans. Amer. Math. Soc. 166 (1972), 215-224
MSC: Primary 57A15
Erratum: Trans. Amer. Math. Soc. 177 (1973), 505.
MathSciNet review: 0295314
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Abstract: In this paper we prove that any upper semicontinuous decomposition of $ E^n$ which is generated by a trivial defining sequence of cubes with handles determines a factor of $ E^{n + 1}$. An important corollary to this result is that every 0-dimensional point-like decomposition of $ E^3$ determines a factor of $ E^4$. In our approach we have simplified the construction of the sequence of shrinking homeomorphisms by eliminating the necessity of shrinking sets piecewise in a collection of n-cells, the technique employed by R. H. Bing in the original result of this type.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0295314-X
PII: S 0002-9947(1972)0295314-X
Keywords: Cubes with handles, defining sequence, trivial defining sequence, universal covering space, 0-dimensional decomposition, point-like decomposition, cell-like spaces, property UV$ ^\infty$
Article copyright: © Copyright 1972 American Mathematical Society