Work

Cardinal inequalities involving the weak Rothberger and cellularity games

Year: 2024

Type: article

Abstract: We prove several results in the theory of topological cardinal invariants involving the game-theoretic versions of the weak Lindelöf degree and of cellularity. One of them is related to Bell, Ginsburg and Woods’s 1978 question of whether every weakly Lindelöf regular first-countable space has cardinality at most continuum and another one is connected with Arhangel’skii’s 1970 question on the weak Lindelöf degree of the $$G_\delta $$ G δ topology on a compact space. We provide a few application of our results, including some bounds on the cardinality of sequential and radial spaces. We finish with a series of counterexamples, which show the sharpness of our results and disprove a few natural conjectures about the impact of infinite games on topological cardinal invariants.

Source: Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas

DOI: 10.1007/s13398-024-01667-z

Authors: Angelo Bella, Lucas Chiozini, Santi Spadaro

Institutions: University of Catania, University of Palermo

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290