2026/04/26 by Souvik Mandal, Ankur Sarkar · 1 voice
Mathematics · #math.GN
Game-theoretic characterizations of selection principles provide a powerful framework for analyzing covering properties through strategic interactions. For a Tychonoff space X and a non-trivial metrizable arc-connected topological group G, we prove that Player~II has a winning strategy in the Ω-Menger game on X if and only if Player~II has a winning strategy in the countable fan tightness game on Cp(X, G) at the identity function. The analogous equivalence is established between the Ω-Rothberger game on X and the countable strong fan tightness game on Cp(X, G) at the identity function. These results extend the game-theoretic characterizations of Clontz from G = ℝ to arbitrary metrizable arc-connected groups, and lift the selection-principle equivalences of Kočinac to the game-theoretic setting. As consequences, we establish that the game-theoretic tightness properties of Cp(X,G) are independent of G, preserved under G-equivalence, and remain valid for Markov strategies.