Products of sequential convergence properties
Two-fold theorem on Fréchetness of products
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.
Weak selections and flows in networks
We demonstrate that every Vietoris continuous selection for the hyperspace of at most 3-point subsets implies the existence of a continuous selection for the hyperspace of at most 4-point subsets. However, in general, we do not know if such ``extensions'' are possible for hyperspaces of sets of other cardinalities. In particular, we do not know if the hyperspace of at most 3-point subsets has a continuous selection provided the hyperspace of at most 2-point subsets has a continuous selection.
Normal subspaces in products of two ordinals
Let λ be an ordinal number. It is shown that normality, collectionwise normality and shrinking are equivalent for all subspaces of .
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