A construction of a CW-decomposition of s-cubes which are manifolds. (English) Zbl 0617.57014

In the paper by M. Božek and the author [Acta Math. Univ. Comenianae 46/47, 7-11 (1985; see the preceding review)] a CW- decomposition \({\mathcal F}^ n\) of the n-dimensional cube \(I^ n\) is introduced in such a way that for any given s-cube \(X=I^ n/(u^ 1,...,u^ n)\) the equivalence relation T is a cellular one on the CW- space \((I^ n, {\mathcal F}^ n)\), and a CW-decomposition \({\mathcal F}^ n/T\) of \(I^ n/T\) is constructed. In the present paper a construction of a simpler CW-decomposition \({\mathcal H}\) of those s-cubes which are manifolds is given. The number of cells of \({\mathcal H}\) is much smaller than that of \({\mathcal F}^ n\).


57N99 Topological manifolds
54B15 Quotient spaces, decompositions in general topology
57Q05 General topology of complexes
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