Soft bornology

In this paper we present the parameterized extension of the concept of bornology. In doing so, we introduce the notions of soft bornology and an M-valued soft bornology where the parametrization plays the key role. Furthermore, we introduce boundedness and parameterized degree of boundedness for soft sets in such spaces, respectively. We observe some of the elementary properties of the proposed spaces. Finally, we looked bounded soft mappings in the corresponding spaces.Publisher's Versio

Bornological structures on many-valued sets

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