{"article_processing_charge":"Yes (via OA deal)","title":"Coarse infinite-dimensionality of hyperspaces of finite subsets","file_date_updated":"2022-01-10T08:33:22Z","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"date_created":"2022-01-09T23:01:27Z","language":[{"iso":"eng"}],"day":"30","file":[{"content_type":"application/pdf","file_name":"2021_EuJournalMath_Weighill.pdf","relation":"main_file","checksum":"c435dcfa1ad3aadc5cdd7366bc7f4e98","creator":"cchlebak","file_size":384908,"date_created":"2022-01-10T08:33:22Z","date_updated":"2022-01-10T08:33:22Z","access_level":"open_access","success":1,"file_id":"10610"}],"article_type":"original","publisher":"Springer Nature","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"abstract":[{"lang":"eng","text":"We consider infinite-dimensional properties in coarse geometry for hyperspaces consisting of finite subsets of metric spaces with the Hausdorff metric. We see that several infinite-dimensional properties are preserved by taking the hyperspace of subsets with at most n points. On the other hand, we prove that, if a metric space contains a sequence of long intervals coarsely, then its hyperspace of finite subsets is not coarsely embeddable into any uniformly convex Banach space. As a corollary, the hyperspace of finite subsets of the real line is not coarsely embeddable into any uniformly convex Banach space. It is also shown that every (not necessarily bounded geometry) metric space with straight finite decomposition complexity has metric sparsification property."}],"date_published":"2021-12-30T00:00:00Z","oa_version":"Published Version","department":[{"_id":"HeEd"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","author":[{"full_name":"Weighill, Thomas","last_name":"Weighill","first_name":"Thomas"},{"full_name":"Yamauchi, Takamitsu","first_name":"Takamitsu","last_name":"Yamauchi"},{"full_name":"Zava, Nicolò","first_name":"Nicolò","last_name":"Zava","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad"}],"date_updated":"2022-01-10T08:36:55Z","has_accepted_license":"1","doi":"10.1007/s40879-021-00515-3","quality_controlled":"1","year":"2021","_id":"10608","ddc":["500"],"scopus_import":"1","month":"12","publication":"European Journal of Mathematics","citation":{"chicago":"Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” <i>European Journal of Mathematics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s40879-021-00515-3\">https://doi.org/10.1007/s40879-021-00515-3</a>.","ama":"Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces of finite subsets. <i>European Journal of Mathematics</i>. 2021. doi:<a href=\"https://doi.org/10.1007/s40879-021-00515-3\">10.1007/s40879-021-00515-3</a>","apa":"Weighill, T., Yamauchi, T., &#38; Zava, N. (2021). Coarse infinite-dimensionality of hyperspaces of finite subsets. <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-021-00515-3\">https://doi.org/10.1007/s40879-021-00515-3</a>","ieee":"T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of hyperspaces of finite subsets,” <i>European Journal of Mathematics</i>. Springer Nature, 2021.","short":"T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics (2021).","ista":"Weighill T, Yamauchi T, Zava N. 2021. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics.","mla":"Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” <i>European Journal of Mathematics</i>, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s40879-021-00515-3\">10.1007/s40879-021-00515-3</a>."},"publication_status":"published","status":"public","acknowledgement":"We would like to thank the referees for their careful reading and the comments that improved our work. The third named author would like to thank the Division of Mathematics, Physics and Earth Sciences of the Graduate School of Science and Engineering of Ehime University and the second named author for hosting his visit in June 2018. Open access funding provided by Institute of Science and Technology (IST Austria)."}