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

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Farkas_2020_Mathematika_Schmidt_sgame_AAM.pdf (287.8Kb)
Date
29/12/2020
Author
Farkas, Ábel
Fraser, Jonathan
Nesharim, Erez
Simmons, David
Keywords
Schmidt's game
Dimension
QA Mathematics
T-NDAS
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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.
Citation
Farkas , Á , Fraser , J , Nesharim , E & Simmons , D 2020 , ' Schmidt's game on Hausdorff metric and function spaces : generic dimension of sets and images ' , Mathematika , vol. 67 , no. 1 , pp. 196-213 . https://doi.org/10.1112/mtk.12068
Publication
Mathematika
Status
Peer reviewed
DOI
https://doi.org/10.1112/mtk.12068
ISSN
0025-5793
Type
Journal article
Rights
Copyright © 2020 The Authors. The publishing rights for this article are licensed to University College London under an exclusive licence. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1112/mtk.12068
Description
AF was financially supported by an ERC Consolidator Grant (772466) and by The MTA Momentum Project (LP2016‐5). JMF was financially supported by a Leverhulme Trust Research Fellowship (RF‐2016‐500) and an EPSRC Standard Grant (EP/R015104/1). EN and DS were supported by an EPSRC Programme Grant (EP/J018260/1).
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  • University of St Andrews Research
URL
https://arxiv.org/abs/1907.07394
URI
http://hdl.handle.net/10023/21233

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