$\alpha_3$; $\alpha_4$; $\beta_3$; $\beta_4$ spaces; $\Phi$-space; product space; sequential space; sequentially subtransverse; strongly Fréchet; transverse
A refined common generalization of known theorems (Arhangel’skii, Michael, Popov and Rančin) on the Fréchetness of products is proved. A new characterization, in terms of products, of strongly Fréchet topologies is provided.
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