Bella, Angelo More on the product of pseudo radial spaces. (English) Zbl 0772.54020 Commentat. Math. Univ. Carol. 32, No. 1, 125-128 (1991). The main question is when the product of pseudo radial spaces is pseudo radial. The main theorem is that the product of a compact pseudo radial space and a compact monolithic pseudo radial space is pseudo radial.Here are the definitions needed: Generalize the notion of a sequence to include \(\kappa\)-sequences, and convergence to include convergence by \(\kappa\)-sequences, where the sequence \(\{x_ \alpha\): \(\alpha<\kappa\}\) converges to \(p\) iff every neighborhood of \(p\) contains a set of the form \(\{x_ \alpha\): \(\beta\leq\alpha <\kappa\}\). A pseudo radial space is one in which every subset \(A\) which is not closed contains a sequence which converges outside of \(A\). A space \(X\) is monolithic iff \(| A|\geq \text{nw}(\text{cl }A)\) for every subset \(A\) of \(X\).The proof also uses the notion of the chain character of a pseudo radial space, i.e. the smallest \(\kappa\) so that if \(A\) is not closed then there is a \(\leq\kappa\)-sequence in \(A\) converging to some point not in \(A\). Reviewer: J.Roitman (Lawrence) Cited in 4 Documents MSC: 54D55 Sequential spaces 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 54B10 Product spaces in general topology Keywords:compact pseudo radial space; compact monolithic pseudo radial space PDFBibTeX XMLCite \textit{A. Bella}, Commentat. Math. Univ. Carol. 32, No. 1, 125--128 (1991; Zbl 0772.54020) Full Text: EuDML