Schmidt's game on Hausdorff metric and function spaces: generic dimension of sets and images
Metric Geometry
2021-03-26 v3
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.
Keywords
Cite
@article{arxiv.1907.07394,
title = {Schmidt's game on Hausdorff metric and function spaces: generic dimension of sets and images},
author = {Ábel Farkas and Jonathan M. Fraser and Erez Nesharim and David Simmons},
journal= {arXiv preprint arXiv:1907.07394},
year = {2021}
}
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21 pages