Whereas the Gerlits-Nagy γ property is strictly weaker than the Galvin-Miller strong γ property, the corresponding strong notions for the Menger, Hurewicz, Rothberger, Gerlits-Nagy (∗), Arkhangel’skǐi and Sakai properties are equivalent to the original ones. We give new game theoretic characterizations for most of these properties, solve a related problem of Kočinac and Scheepers, and answer a ...

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Arhangel’skii proved that if a first countable Hausdorff space is Lindelöf, then its cardinality is at most 20 . Such a clean upper bound for Lindelöf spaces in the larger class of spaces whose points are Gδ has been more elusive. In this paper we continue the agenda started in [50], of considering the cardinality problem for spaces satisfying stronger versions of the Lindelöf property. Infinit...

A local search method is developed and applied to create trajectories over S-box spaces in this work. These show a strong linear correlation between confusion coefficient variance, transparency order, modified revised order under the Hamming weight model. When variance values increase, of beta zero, zero decrease, reflecting same theoretical resistance against side-channel attacks by power cons...

We present a new characterization of Erd?s space factors, and show that the $$\mathfrak{C}$$ is unstable in class almost zero-dimensional F??-spaces. The latter answers question by Dijkstra van Mill.