An algebraic version of Tamano's theorem for countably compact spaces (Q989110)

The author shows that if a space \(X\) is countably compact but not compact then one can find a compact space \(K\) such that \(X + K\) does not embed closedly into any normal topological group. Additionally she proves that for a countably compact space \(X\), which is not compact, no normal topological group contains a closed copy of \(X + (\tau\;+ 1)\), where \(\tau\) is the successor cardinal of \(\beta\,\, X \) and \(\beta\,\, X\) denotes the Stone-Čech compactification of \(X\). At last it is proved that if the cross-product of a space X is countably compact and normal and X not compact then no normal topological group contains a closed copy of \(X\) + \(bX\), where \(bX\) is an arbitrary Hausdorff compactification of \(X\).