# '22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

### "Coverings of Banach spaces and their subsets by hyperplanes"

#### Głodkowski, Damian

A hyperplane of a Banach space is a closed one-codimensional subspace. For a Banach space $X$ we consider the $\sigma$-ideal of all subsets of $X$ that can be covered by countably many hyperplanes and investigate its standard cardinal characteristics i.e. the additivity, the covering number, the uniformity, the cofinality. We completely determine their values for separable Banach spaces in ZFC, and for all nonseparable Banach spaces under additional assumptions such as GCH or MM. We also find an application of our results to the topic of overcomplete sets in Banach spaces. This is joint work with Piotr Koszmider.

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