Categorical foundations of variety-based bornology

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Authors	PASEKA Jan SOLOVJOVS Sergejs
Year of publication	2016
Type	Article in Periodical
Magazine / Source	Fuzzy Sets and Systems
MU Faculty or unit	Faculty of Science
Citation
Doi	https://doi.org/10.1016/j.fss.2015.07.011
Field	General mathematics
Keywords	Bornological space; Bornological system; Bornological theory; Ideal; Powerset theory; Reflective subcategory; System spatialization procedure; Topological category; Variety of algebras
Attached files	On_a_topological_universe_of_L-bornological_spaces_final.pdf
Description	Following the concept of topological theory of S.E. Rodabaugh, this paper introduces a new approach to (lattice-valued) bornology, which is based in bornological theories, and which is called variety-based bornology. In particular, motivated by the notion of topological system of S. Vickers, we introduce the concept of variety-based bornological system, and show that the category of variety-based bornological spaces is isomorphic to a full reflective subcategory of the category of variety-based bornological systems. (C) 2015 Elsevier B.V. All rights reserved.
Related projects:	New approaches to residuated posets