Cartesian products of Fréchet topological groups and function spaces (Q1207365)

The authors consider the behavior of the convergence properties under products in topological groups and in function spaces. Adding a single Cohen real to a model of \(\text{MA}+\neg\text{CH}\), they construct a model in which there exist: (1) a topological group \(G\) such that \(G\) is hereditarily separable and Fréchet, but \(G\times G\) has uncountable tightness, and (2) Tychonoff spaces \(X\) and \(Y\) such that \(C_ p(X)^ \omega\) and \(C_ p(Y)^ \omega\) are hereditarily separable, but \(C_ p(X)\times C_ p(Y)\) has uncountable tightness (\(C_ p(X)\) is the space of continuous functions in pointwise convergence topology and \(C_ p(X)^ \omega\) denotes the \(\omega\)-th power of this space).