Countably compact groups and \(p\)-limits (Q1429078)

The paper contains three examples in the proofs of the following theorems: Theorem (1.6). \([\mathfrak p=\mathfrak c]\) There exists a selective ultrafilter \(p\in \omega^*\) and an almost p-compact topological group whose square is not countably compact. Theorem (1.11). It is consistent with ZFC that there exists a countably compact topological group which is not quasi M-compact for any \(M\in [\omega^*]^{<2^{\mathfrak c}}\). Theorem (1.13). It is consistent that there exists a family of topological groups \({G_\alpha : \alpha <2^{\mathfrak c }}\) such that for a subset I of \(2^{\mathfrak c}\), \(\prod_{\alpha\in I} G_\alpha\) is countably compact if and only if \(| I| <2^{\mathfrak c}\).