2017/06/15 by S. Garcı́a-Ferreira, Garcia-Ferreira, S., Artur Hideyuki Tomita +1
Mathematics · Computer Science · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1706.04911
A space X is called \it selectively pseudocompact if for each sequence (Un)n∈ ℕ of pairwise disjoint nonempty open subsets of X there is a sequence (xn)n∈ ℕ of points in X such that clX(\xn : n < ω\) ∖ (\bigcupn < ωUn ) ≠ ∅ and xn∈ Un, for each n < ω. Countably compact space spaces are selectively pseudocompact and every selectively pseudocompact space is pseudocompact. We show, under the assumption of CH, that for every positive integer k > 2 there exists a topological group whose k-th power is countably compact but its (k+1)-st power is not selectively pseudocompact. This provides a positive answer to a question posed in \citegt in any model of ZFC+CH.