Homogeneous products of spaces (Q1382561)

The author presents results similar to Uspenskij's theorem [\textit{V. V. Uspenskij}, Proc. Am. Math. Soc. 87, 187-188 (1983; Zbl 0504.54007)]. For some classes of spaces it is proved that for \(X\in\mathcal P\) there exists a homogeneous space \(H\in\mathcal P\) such that \(X\times H\) is homeomorphic to \(H\). An example of a homogeneous space of countable closeness is considered where the space is not \(p\)-sequential for any ultrafilter \(p\in\beta\omega/\omega\).