# Order-Topological lattices

 dc.identifier.uri http://dx.doi.org/10.15488/2696 dc.identifier.uri http://www.repo.uni-hannover.de/handle/123456789/2722 dc.contributor.author Erné, Marcel dc.date.accessioned 2018-01-29T14:13:18Z dc.date.available 2018-01-29T14:13:18Z dc.date.issued 1980 dc.identifier.citation Erné, Marcel: Order-Topological lattices. In: Glasgow Mathematical Journal 21 (1980), Nr. 1, S. 57-68. DOI: https://doi.org/10.1017/S0017089500003980 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.relation.doi https://doi.org/10.1017/S0017089500003980 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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