A Borsuk-Ulam theorem for maps from a sphere to a generalized manifold. (Q1768271)

By removing differentiability assumptions, \textit{H. Munkholm} [Ill. J. Math. 13, 116--124 (1969; Zbl 0164.53801)] generalized to compact topological manifolds a Borsuk-Ulam type theorem first proved by \textit{P. E. Conner} and \textit{E. E. Floyd} [Differentiable periodic maps, Springer-Verlag (1964; Zbl 0125.40103)]. By a generalized manifold, we mean a Euclidean neighborhood retract \(X\) which is locally a homology manifold over \(\mathbb Z_2\), i.e., \(H_*(X,X-\{x\};\mathbb Z_2) \cong H_*(\mathbb R^m,\mathbb R^m-\{0\};\mathbb Z_2)\) for every \(x\in X\). In the paper under review, the authors prove a similar Borsuk-Ulam type theorem for generalized manifolds, using a notion of Stiefel-Whitney classes for generalized manifolds introduced by \textit{C. Biasi, J. Daccach} and \textit{O. Saeki} [Pac. J. Math. 197, No. 2, 275--289 (2001; Zbl 1051.57030)].