Rosicki, Witold On decomposition of polyhedra into a Cartesian product of 1-dimensional and 2-dimensional factors. (English) Zbl 0872.57029 Colloq. Math. 72, No. 1, 103-109 (1997). K. Borsuk [Fundam. Math. 31, 137-148 (1938; Zbl 0019.28201)] proved that the decomposition of a polyhedron into a Cartesian product of 1-dimensional factors is topologically unique (up to a permutation of the factors). We prove a little more general Theorem. If a connected polyhedron \(K\) (of arbitrary dimension) is homeomorphic to a Cartesian product \(A_1 \times \cdots \times A_n\), where the \(A_i\)’s are prime compacta of dimension at most 1, then there is no other topologically different system of prime compacta \(Y_1, \dots, Y_k\) of dimension at most 2 such that \(Y_1 \times \cdots \times Y_k\) is homeomorphic to \(K\).A space \(X\) is said to be prime if it has more than one point and only \(X\) and the singleton as Cartesian factors. Cited in 2 Documents MSC: 57Q05 General topology of complexes Keywords:decomposition; polyhedron; Cartesian product Citations:Zbl 0019.28201 PDFBibTeX XMLCite \textit{W. Rosicki}, Colloq. Math. 72, No. 1, 103--109 (1997; Zbl 0872.57029) Full Text: DOI EuDML