Download statistics - Document (COUNTER):

Erné, Marcel: Order-Topological lattices. In: Glasgow Mathematical Journal 21 (1980), Nr. 1, S. 57-68. DOI: https://doi.org/10.1017/S0017089500003980

Repository version

To cite the version in the repository, please use this identifier: https://doi.org/10.15488/2696

Selected time period:

year: 
month: 

Sum total of downloads: 39




Thumbnail
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.
License of this version: 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.
Document Type: article
Publishing status: publishedVersion
Issue Date: 1980
Appears in Collections:Fakultät für Mathematik und Physik

distribution of downloads over the selected time period:

downloads by country:

pos. country downloads
total perc.
1 image of flag of Germany Germany 13 33.33%
2 image of flag of India India 6 15.38%
3 image of flag of France France 3 7.69%
4 image of flag of China China 2 5.13%
5 image of flag of Brazil Brazil 2 5.13%
6 image of flag of Slovenia Slovenia 1 2.56%
7 image of flag of Singapore Singapore 1 2.56%
8 image of flag of Russian Federation Russian Federation 1 2.56%
9 image of flag of Romania Romania 1 2.56%
10 image of flag of Netherlands Netherlands 1 2.56%
    other countries 8 20.51%

Further download figures and rankings:


Hinweis

Zur Erhebung der Downloadstatistiken kommen entsprechend dem „COUNTER Code of Practice for e-Resources“ international anerkannte Regeln und Normen zur Anwendung. COUNTER ist eine internationale Non-Profit-Organisation, in der Bibliotheksverbände, Datenbankanbieter und Verlage gemeinsam an Standards zur Erhebung, Speicherung und Verarbeitung von Nutzungsdaten elektronischer Ressourcen arbeiten, welche so Objektivität und Vergleichbarkeit gewährleisten sollen. Es werden hierbei ausschließlich Zugriffe auf die entsprechenden Volltexte ausgewertet, keine Aufrufe der Website an sich.

Search the repository


Browse