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Daverman, Robert J.; Preston, D. Kriss
Proceedings of the American Mathematical Society, 07/1980, Letnik: 79, Številka: 3Journal Article
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.
