2012/12/22 by Angelo Bella, Bella, Angelo, Santi Spadaro +1
Computer Science · Mathematics · #54D10 #91A44 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Primary: 54A25 #Secondary: 54D35
paper · pdf · doi:10.48550/arxiv.1212.5724
openalex publication_date 2012/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Inspired by work of Scheepers and Tall, we use properties defined by topological games to provide bounds for the cardinality of topological spaces. We obtain a partial answer to an old question of Bell, Ginsburg and Woods regarding the cardinality of weakly Lindelöf first-countable regular spaces and answer a question recently asked by Babinkostova, Pansera and Scheepers. In the second part of the paper we study a game-theoretic version of cellularity, a special case of which has been introduced by Aurichi. We obtain a game-theoretic proof of Shapirovskii's bound for the number of regular open sets in an (almost) regular space and give a partial answer to a natural question about the productivity of a game strengthening of the countable chain condition that was introduced by Aurichi. As a final application of our results we prove that the Hajnal-Juhász bound for the cardinality of a first-countable ccc Hausdorff space is true for almost regular (non-Hausdorff) spaces.