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Bounded Sets in Topological Spaces
dc.contributor.author | Bors, Cristina | |
dc.contributor.author | Ferrer, María V. | |
dc.contributor.author | Hernández, Salvador | |
dc.date.accessioned | 2022-06-08T10:55:13Z | |
dc.date.available | 2022-06-08T10:55:13Z | |
dc.date.issued | 2022-02 | |
dc.identifier.citation | Bors, C.; Ferrer, M.V.; Hernández, S. Bounded Sets in Topological Spaces. Axioms 2022, 11, 71. https://doi.org/10.3390/axioms11020071 | ca_CA |
dc.identifier.issn | 2075-1680 | |
dc.identifier.uri | http://hdl.handle.net/10234/197942 | |
dc.description.abstract | Let G be a monoid that acts on a topological space X by homeomorphisms such that there is a point x0∈X with GU=X for each neighbourhood U of x0. A subset A of X is said to be G-bounded if for each neighbourhood U of x0 there is a finite subset F of G with A⊆FU. We prove that for a metrizable and separable G-space X, the bounded subsets of X are completely determined by the bounded subsets of any dense subspace. We also obtain sufficient conditions for a G-space X to be locally G-bounded, which apply to topological groups. Thereby, we extend some previous results accomplished for locally convex spaces and topological groups. | ca_CA |
dc.format.extent | 8 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | MDPI | ca_CA |
dc.relation.isPartOf | Axioms. 2022; 11(2): 71 | ca_CA |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | ca_CA |
dc.subject | bounded set | ca_CA |
dc.subject | group action | ca_CA |
dc.subject | G-space | ca_CA |
dc.subject | barrelled space | ca_CA |
dc.title | Bounded Sets in Topological Spaces | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.3390/axioms11020071 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | https://www.mdpi.com/2075-1680/11/2/71 | ca_CA |
dc.description.sponsorship | Research partially supported by the Spanish Ministerio de Economía y Competitividad, grant: MTM/PID2019-106529GB-I00 (AEI/FEDER, EU) and by the Universitat Jaume I, grant UJI-B2019-06. | |
dc.type.version | info:eu-repo/semantics/publishedVersion | ca_CA |
project.funder.name | Ministerio de Economía y Competitividad | ca_CA |
project.funder.name | Universitat Jaume I | ca_CA |
oaire.awardNumber | MTM/PID2019-106529GB-I00 | ca_CA |
oaire.awardNumber | UJI-B2019-06 | ca_CA |
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