Rad HAZU, Matematičke znanosti, Vol. 21 (2017), 143-168.

BORNOLOGICAL STRUCTURES ON MANY-VALUED SETS

Alexander Šostak and Ingrīda Uļjane

Department of Mathematics, University of Latvia, LV-1002 Riga, Latvia
and Institute of Mathematics and Computer Sciences UL, LV-1459 Riga, Latvia
e-mail: aleksandrs.sostaks@lu.lv, aleksandrs.sostaks@lumii.lv

Department of Mathematics, University of Latvia, LV-1002 Riga, Latvia
and Institute of Mathematics and Computer Sciences UL, LV-1459 Riga, Latvia
e-mail: ingrida.uljane@lu.lv, ingrida.uljane@lumii.lv

Abstract.   We introduce an approach to the concept of bornology in the framework of many-valued mathematical structures and develop the basics of the theory of many-valued bornological spaces and initiate the study of the category of many-valued bornological spaces and appropriately defined bounded "mappings" of such spaces. A scheme for constructing many-valued bornologies with prescribed properties is worked out. In particular, this scheme allows to extend an ordinary bornology of a metric space to a many-valued bornology on it.

2010 Mathematics Subject Classification.   54A40.

Key words and phrases.   Bornology, quantale, many-valued mathematical structures, many-valued bornology, fuzzy set.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/90836cdw6y

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