Echeloned Spaces
We introduce the notion of echeloned spaces – an order-theoretic abstraction of metric spaces. The first step is to characterize metrizable echeloned spaces. It turns out that morphisms between metrizable echeloned spaces are uniformly continuous or have a uniformly discrete image. In particular, ev...
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425000477/type/journal_article |
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| author | Maxime Gheysens Bojana Pavlica Christian Pech Maja Pech Friedrich Martin Schneider |
| author_facet | Maxime Gheysens Bojana Pavlica Christian Pech Maja Pech Friedrich Martin Schneider |
| author_sort | Maxime Gheysens |
| collection | DOAJ |
| description | We introduce the notion of echeloned spaces – an order-theoretic abstraction of metric spaces. The first step is to characterize metrizable echeloned spaces. It turns out that morphisms between metrizable echeloned spaces are uniformly continuous or have a uniformly discrete image. In particular, every automorphism of a metrizable echeloned space is uniformly continuous, and for every metric space with midpoints, the automorphisms of the induced echeloned space are precisely the dilations. |
| format | Article |
| id | doaj-art-e6bd70d4c0304f4db520065e9c26a5d0 |
| institution | OA Journals |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-e6bd70d4c0304f4db520065e9c26a5d02025-08-20T01:55:31ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2025.47Echeloned SpacesMaxime Gheysens0Bojana Pavlica1https://orcid.org/0000-0002-8080-8610Christian Pech2https://orcid.org/0000-0002-5018-013XMaja Pech3https://orcid.org/0000-0003-3426-199XFriedrich Martin Schneider4https://orcid.org/0000-0002-4126-2758Institute of Discrete Mathematics and Algebra, Faculty of Mathematics and Computer Science, Technische Universität Bergakademie Freiberg, D-09596 Freiberg, Germany; E-mail:Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, 21000 Novi Sad, Serbia; E-mail:Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic; E-mail:Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, 21000 Novi Sad, Serbia; E-mail:Institute of Discrete Mathematics and Algebra, Faculty of Mathematics and Computer Science, Technische Universität Bergakademie Freiberg, D-09596 Freiberg, GermanyWe introduce the notion of echeloned spaces – an order-theoretic abstraction of metric spaces. The first step is to characterize metrizable echeloned spaces. It turns out that morphisms between metrizable echeloned spaces are uniformly continuous or have a uniformly discrete image. In particular, every automorphism of a metrizable echeloned space is uniformly continuous, and for every metric space with midpoints, the automorphisms of the induced echeloned space are precisely the dilations.https://www.cambridge.org/core/product/identifier/S2050509425000477/type/journal_article03C5005D1005C5554E3554E4054H11 |
| spellingShingle | Maxime Gheysens Bojana Pavlica Christian Pech Maja Pech Friedrich Martin Schneider Echeloned Spaces Forum of Mathematics, Sigma 03C50 05D10 05C55 54E35 54E40 54H11 |
| title | Echeloned Spaces |
| title_full | Echeloned Spaces |
| title_fullStr | Echeloned Spaces |
| title_full_unstemmed | Echeloned Spaces |
| title_short | Echeloned Spaces |
| title_sort | echeloned spaces |
| topic | 03C50 05D10 05C55 54E35 54E40 54H11 |
| url | https://www.cambridge.org/core/product/identifier/S2050509425000477/type/journal_article |
| work_keys_str_mv | AT maximegheysens echelonedspaces AT bojanapavlica echelonedspaces AT christianpech echelonedspaces AT majapech echelonedspaces AT friedrichmartinschneider echelonedspaces |