research-article

Lattice-valued bornological systems

Authors:

Sergey A. Solovyov,

Milan StehlíkAuthors Info & Claims

Fuzzy Sets and Systems, Volume 259, Issue C

Pages 68 - 88

https://doi.org/10.1016/j.fss.2014.09.006

Published: 15 January 2015 Publication History

Abstract

Motivated by the concept of lattice-valued topological system of J.T. Denniston, A. Melton, and S.E. Rodabaugh, which extends lattice-valued topological spaces, this paper introduces the notion of lattice-valued bornological system as a generalization of lattice-valued bornological spaces of M. Abel and A. Šostak. We aim at (and make the first steps towards) the theory, which will provide a common setting for both lattice-valued point-set and point-free bornology. In particular, we show the algebraic structure of the latter.

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Cited By

Jin ZYan C(2022)Fuzzifying bornological linear spacesJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-21164442:3(2347-2358)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.3233/JIFS-211644
Jin ZYan C(2021)Induced L-bornological vector spaces and L-Mackey convergence1 Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-20159940:1(1277-1285)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.3233/JIFS-201599
Denniston JMelton ARodabaugh SSolovyov S(2016)Topological systems as a framework for institutionsFuzzy Sets and Systems10.1016/j.fss.2015.08.009298:C(91-108)Online publication date: 1-Sep-2016
https://dl.acm.org/doi/10.1016/j.fss.2015.08.009
Show More Cited By

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Published In

cover image Fuzzy Sets and Systems

Fuzzy Sets and Systems Volume 259, Issue C

January 2015

128 pages

ISSN:0165-0114

Issue’s Table of Contents

Copyright © Elsevier B.V.

Publisher

Elsevier North-Holland, Inc.

United States

Publication History

Published: 15 January 2015

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Cited By

Jin ZYan C(2022)Fuzzifying bornological linear spacesJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-21164442:3(2347-2358)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.3233/JIFS-211644
Jin ZYan C(2021)Induced L-bornological vector spaces and L-Mackey convergence1 Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-20159940:1(1277-1285)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.3233/JIFS-201599
Denniston JMelton ARodabaugh SSolovyov S(2016)Topological systems as a framework for institutionsFuzzy Sets and Systems10.1016/j.fss.2015.08.009298:C(91-108)Online publication date: 1-Sep-2016
https://dl.acm.org/doi/10.1016/j.fss.2015.08.009
Paseka JSolovyov S(2016)Categorical foundations of variety-based bornologyFuzzy Sets and Systems10.1016/j.fss.2015.07.011291:C(132-143)Online publication date: 15-May-2016
https://dl.acm.org/doi/10.1016/j.fss.2015.07.011
Paseka JSolovyov SStehlík M(2016)On a topological universe of L-bornological spacesSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-015-1905-020:7(2503-2512)Online publication date: 1-Jul-2016
https://dl.acm.org/doi/10.1007/s00500-015-1905-0

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