Farkas, Ábel and Fraser, Jonathan M. and Nesharim, Erez and Simmons, David (2021) SCHMIDT'S GAME ON HAUSDORFF METRIC AND FUNCTION SPACES: GENERIC DIMENSION OF SETS AND IMAGES. MATHEMATIKA, 67 (1). pp. 196-213. ISSN 0025-5793
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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 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. © 2020 The Authors. The publishing rights for this article are licensed to University College London under an exclusive licence.
| Item Type: | Article |
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| Additional Information: | Export Date: 16 April 2021 Correspondence Address: Nesharim, E.; Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram 9190401, Israel; email: ereznesh@gmail.com Funding details: European Research Council, ERC Funding text 1: We would like to thank the anonymous referee for the thorough readthrough and useful comments. This work began during the semester programme on Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism hosted by ICERM in Spring 2016. It continued at the semester programme on Fractal Geometry and Dynamics hosted by the Institut Mittag-Leffler in Fall?2017. Funding text 2: ERC Consolidator Grant The MTA Momentum Project Leverhulme Trust Research Fellowship EPSRC Standard Grant |
| Uncontrolled Keywords: | 28A78; 28A80; 91A05 (secondary); 91A44 (primary); |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 16 Apr 2021 13:15 |
| Last Modified: | 16 Apr 2021 13:15 |
| URI: | http://real.mtak.hu/id/eprint/123924 |
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