Frolík, Zdeněk; Tironi, Gino Products of chain-net spaces. (English) Zbl 0705.54020 Riv. Mat. Pura Appl. 5, 7-11 (1989). A topological space X is said to be chain-net or pseudoradial if for any nonclosed subset A of X, there exists a point \(x\in \bar A\setminus A\) and a \(\lambda\)-sequence \((x_{\alpha})_{\alpha <\lambda},x_{\alpha}\in A\), converging to x. A space is Fréchet chain-net or radial if for every point \(x\in A\) there is a \(\lambda\)- sequence of elements of A converging to it. It is well known that the product of two chain-net (or pseudoradial) spaces is, in general, not chain-net. The authors prove that the product of two chain-net compact Hausdorff spaces is chain-net if one of them is radial. Cited in 1 ReviewCited in 4 Documents MSC: 54D55 Sequential spaces 54B10 Product spaces in general topology 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) Keywords:chain-net (pseudoradial) spaces; Fréchet chain-net (radial) spaces; \(\lambda \) -sequence; chain-net compact Hausdorff spaces PDFBibTeX XMLCite \textit{Z. Frolík} and \textit{G. Tironi}, Riv. Mat. Pura Appl. 5, 7--11 (1989; Zbl 0705.54020)