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dc.identifier.uri Erné, Marcel 2018-01-29T14:13:18Z 2018-01-29T14:13:18Z 1980
dc.identifier.citation Erné, Marcel: Order-Topological lattices. In: Glasgow Mathematical Journal 21 (1980), Nr. 1, S. 57-68. DOI:
dc.description.abstract The observation that convergence of real sequences may be defined in terms of limits inferior and limits superior as by means of neighbourhoods in the Euclidean topology leads to the question: for which lattices does order convergence coincide with convergence in the order topology? This problem has been attacked by D. C. Kent [10], A. Gingras [7] and others. We hope to present a satisfactory solution in this paper. Although there are known several characterizations of lattices, with topological order convergence (cf. Propositions 1, 2), an evaluation of these criteria already requires some knowledge of the order topology of the given lattice. In the present paper, we establish a purely lattice-theoretical description of those lattices for which order convergence is not only topological, but moreover, the lattice operations are continuous. Henceforth, such lattices will be referred to as order-topological lattices. All convergence statements will be formulated in terms of filters rather than nets. For an introduction to convergence functions, the reader may consult D. C. Kents's paper [9]. © 1980, Glasgow Mathematical Journal Trust. All rights reserved. eng
dc.language.iso eng
dc.publisher Cambridge : Cambridge University Press
dc.relation.ispartofseries Glasgow Mathematical Journal 21 (1980), Nr. 1
dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
dc.subject lattice eng
dc.subject Gingras eng
dc.subject Kent eng
dc.subject.ddc 510 | Mathematik ger
dc.title Order-Topological lattices
dc.type article
dc.type Text
dc.relation.issn 0017-0895
dc.bibliographicCitation.issue 1
dc.bibliographicCitation.volume 21
dc.bibliographicCitation.firstPage 57
dc.bibliographicCitation.lastPage 68
dc.description.version publishedVersion
tib.accessRights frei zug�nglich

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