A general class of factors of 𝐸⁴

Rubin, Leonard R.

doi:10.1090/S0002-9947-1972-0295314-X

A general class of factors of $E^4$
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Trans. Amer. Math. Soc. 166 (1972), 215-224 Request permission

Erratum: Trans. Amer. Math. Soc. 177 (1973), 505.

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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