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BORNOLOGIES AND LOCALLY LIPSCHITZ FUNCTIONS

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dc.contributor.authorGarrido, M. Isabel
dc.date.accessioned2023-06-19T13:28:23Z
dc.date.available2023-06-19T13:28:23Z
dc.date.issued2014
dc.description.abstractLet hX, di be a metric space. We characterise the family of subsets of X on which each locally Lipschitz function defined on X is bounded, as well as the family of subsets on which each member of two different subfamilies consisting of uniformly locally Lipschitz functions is bounded. It suffices in each case to consider real-valued functions.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/28548
dc.identifier.doi10.1017/S0004972714000215
dc.identifier.issn0004-9727
dc.identifier.officialurlhttp://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9332599&fulltextType=RA&fileId=S0004972714000215
dc.identifier.relatedurlhttp://journals.cambridge.org/action/displayJournal?jid=BAZ
dc.identifier.urihttps://hdl.handle.net/20.500.14352/33803
dc.issue.number2
dc.journal.titleBulletin of the Australian Mathematical Society
dc.language.isoeng
dc.page.final263
dc.page.initial257
dc.publisherAustralian Mathematical Society
dc.rights.accessRightsrestricted access
dc.subject.cdu515.1
dc.subject.keywordLipschitz function
dc.subject.keywordLocally Lipschitz function
dc.subject.keywordUniformly locally Lipschitz
dc.subject.keywordFunction
dc.subject.keywordLipschitz in the small function
dc.subject.keywordfunction preserving Cauchy sequences
dc.subject.keywordbornology
dc.subject.keywordtotally bounded set
dc.subject.keywordBourbaki bounded set
dc.subject.ucmTopología
dc.subject.unesco1210 Topología
dc.titleBORNOLOGIES AND LOCALLY LIPSCHITZ FUNCTIONS
dc.typejournal article
dc.volume.number90
dcterms.referencesM. Atsuji, ‘Uniform continuity of continuous functions of metric spaces’, Pacific J. Math. 8 (1958), 11–16. G. Beer, Topologies on Closed and Closed Convex Sets (Kluwer Academic, Dordrecht, The Netherlands, 1993). G. Beer, ‘Embeddings of bornological universes’, Set-Valued Anal. 16 (2008), 477–488. G. Beer and S. Levi, ‘Total boundedness and bornologies’, Topology Appl. 156 (2009), 1271–1288. N. Bourbaki, Elements of Mathematics. General Topology. Part 1 (Hermann, Paris, 1966). A. Caserta, G. Di Maio and L. Hola, ‘Arzel ´ a’s theorem and strong uniform convergence on ` bornologies’, J. Math. Anal. Appl. 371 (2010), 384–392. R. Engelking, General Topology (Polish Scientific Publishers, Warsaw, 1977). M. I. Garrido and J. Jaramillo, ‘Homomorphisms on function lattices’, Monatsh. Math. 141 (2004), 127–146. M. I. Garrido and J. Jaramillo, ‘Lipschitz-type functions on metric spaces’, J. Math. Anal. Appl. 340 (2008), 282–290. M. I. Garrido and A. S. Merono, ‘New types of completeness in metric spaces’, ˜ Ann. Acad. Sci. Fenn. Math. to appear. R. Goldberg, Methods of Real Analysis, 2nd edn (Wiley, New York, 1976). J. Hejcman, ‘Boundedness in uniform spaces and topological groups’, Czech. Math. J. 9 (1959), 544–563. H. Hogbe-Nlend, Bornologies and Functional Analysis (North-Holland, Amsterdam, 1977). A. Roberts and D. Varberg, Convex Functions (Academic Press, New York, 1973). A. Taylor and D. Lay, Introduction to Functional Analysis, 2nd edn (Wiley, New York, 1980). T. Vroegrijk, ‘Uniformizable and realcompact bornological universes’, Appl. Gen. Topol. 10 (2009), 277–287.
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