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arXiv · 1907.07394

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

Ábel Farkas·Jonathan M. Fraser·Erez Nesharim·David Simmons
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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 behaviour 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.

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Ábel Farkas, Jonathan M. Fraser, Erez Nesharim, David Simmons. 2021-02-02. Schmidt's game on Hausdorff metric and function spaces: generic dimension of sets and images. https://arxiv.org/abs/1907.07394

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