Leírás
Speaker: Lucas Chiozini
Title: On the use of topological games on cardinal function inequalities
Some of the most famous results regarding cardinal functions consist in using them to provide an upper bound to the cardinality of some classes of spaces, such as Arhangel’skii’s theorem and Hajnal-Juhász’ inequality, both true for Hausdorff spaces.
These results have spawned a number of questions, such as Arhangel’skii’s problem whether there is an upper bound to Lindelöf spaces with points G_δ and, in recent years, many authors have used infinite topological games to give partial answers to these problems.
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In this talk, we want to discuss some of our successes in refining previously known results and inequalities in this field by using the weak Rothberger game and the cellularity game, as well as provide a few examples which illustrate their sharpness whenever possible.