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Schmidt's game on Hausdorff metric and function spaces: generic dimension of sets and images | | Ábel Farkas
; Jonathan M. Fraser
; Erez Nesharim
; David Simmons
; | | Date: |
17 Jul 2019 | | 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. | | Source: | arXiv, 1907.7394 | | Services: | Forum | Review | PDF | Favorites | |
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