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Products of chain-net spaces. (English) Zbl 0705.54020

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.

MSC:

54D55 Sequential spaces
54B10 Product spaces in general topology
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
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