Schmidt's game on Hausdorff metric and function spaces: generic dimension of sets and images

Ábel Farkas, Jonathan Fraser, Erez Nesharim, David Simmons

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We consider Schmidt's game on the space of compact subsets of a given metric space equipped with the Hausdorff metric, and the space of continuous functions equipped with the supremum norm. We are interested in determining the generic behavior of objects in a metric space, mostly in the context of fractal dimensions, and the notion of “generic” we adopt is that of being winning for Schmidt's game. We find properties whose corresponding sets are winning for Schmidt's game that are starkly different from previously established, and well‐known, properties which are generic in other contexts, such as being residual or of full measure.
Original languageEnglish
Pages (from-to)196-213
JournalMathematika
Volume67
Issue number1
DOIs
Publication statusPublished - 29 Dec 2020

Keywords

  • Schmidt's game
  • Dimension

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