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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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Keywords: Cubes with handles, defining sequence, trivial defining sequence, universal covering space, 0-dimensional decomposition, point-like decomposition, cell-like spaces, property <!– MATH $\text {UV}^\infty$ –> UV<IMG WIDTH="23" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$^\infty$">
Article copyright: © Copyright 1972 American Mathematical Society