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Soft Computing
Published in: Soft Computing 7/2016

05-11-2015 | Foundations

On a topological universe of L-bornological spaces

Authors: Jan Paseka, Sergey A. Solovyov, Milan Stehlík

Published in: Soft Computing | Issue 7/2016

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Abstract

This paper shows that given a certain frame L, the construct of strict L-bornological spaces, introduced by Abel and Šostak, is a topological universe.
next article On Carlson’s inequality for Sugeno and Choquet integrals

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Literature
Abel M, Šostak A (2011) Towards the theory of \(L\)-bornological spaces. Iran J Fuzzy Syst 8(1):19–28MathSciNetMATH
Adámek J, Herrlich H, Strecker GE (2009) Abstract and concrete categories: the joy of cats. Dover Publications, New YorkMATH
Birkhoff G (1979) Lattice theory, 3rd edn. American Mathematical Society Colloquium Publications, vol. XXV. American Mathematical Society
Engelking R (1989) General topology. Heldermann Verlag
Gierz G, Hofmann KH et al (2003) Continuous lattices and domains. Cambridge University Press, CambridgeCrossRefMATH
Hermann P, Mrkvička T, Mattfeldt T, Minárová M, Helisová K, Nicolis O, Wartner F, Stehlík M (2015) Fractal and stochastic geometry inference for breast cancer: a case study with random fractal models and Quermass-interaction process. Stat Med 34(18):2636–2661MathSciNetCrossRef
Hogbe-Nlend H (1977) Bornologies and functional analysis. Mathematics Studies, vol. 26. North-Holland Publishing Company
Höhle U, Šostak AP (1999) Axiomatic foundations of fixed-basis fuzzy topology. In: Höhle U, Rodabaugh SE (eds) Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory. Kluwer Academic Publishers, pp 123–272
Johnstone PT (1982) Stone spaces. Cambridge University Press, CambridgeMATH
Liu YM, Luo MK (1997) Fuzzy topology. World Scientific Publishing Co
Paseka J, Solovyov S, Stehlík M (2015) Lattice-valued bornological systems. Fuzzy Sets Syst 259:68–88
Rodabaugh SE (1999) Categorical foundations of variable-basis fuzzy topology. In: Höhle U, Rodabaugh SE (eds) Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory. Kluwer Academic Publishers, pp 273–388
Rodabaugh SE (1999) Powerset operator foundations for poslat fuzzy set theories and topologies. In: Höhle U, Rodabaugh SE (eds) Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory. Kluwer Academic Publishers, pp 91–116
Metadata
Title
On a topological universe of L-bornological spaces
Authors
Jan Paseka
Sergey A. Solovyov
Milan Stehlík
Publication date
05-11-2015
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 7/2016
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-015-1905-0

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