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Schmidt's game on Hausdorff metric and function spaces : generic dimension of sets and images
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dc.contributor.author | Farkas, Ábel | |
dc.contributor.author | Fraser, Jonathan | |
dc.contributor.author | Nesharim, Erez | |
dc.contributor.author | Simmons, David | |
dc.date.accessioned | 2021-01-07T09:30:18Z | |
dc.date.available | 2021-01-07T09:30:18Z | |
dc.date.issued | 2020-12-29 | |
dc.identifier | 271171320 | |
dc.identifier | 0e5e02d0-b260-474d-9214-30dd30be8f8e | |
dc.identifier | 85099806498 | |
dc.identifier | 000614532000011 | |
dc.identifier.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 | en |
dc.identifier.issn | 0025-5793 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/86538075 | |
dc.identifier.uri | https://hdl.handle.net/10023/21233 | |
dc.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). | en |
dc.description.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. | |
dc.format.extent | 294790 | |
dc.language.iso | eng | |
dc.relation.ispartof | Mathematika | en |
dc.subject | Schmidt's game | en |
dc.subject | Dimension | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Schmidt's game on Hausdorff metric and function spaces : generic dimension of sets and images | en |
dc.type | Journal article | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1112/mtk.12068 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/abs/1907.07394 | en |
dc.identifier.grantnumber | RF-2016-500 | en |
dc.identifier.grantnumber | EP/R015104/1 | en |
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