Categorical foundations of variety-based bornology

• Autoři: PASEKA Jan; SOLOVJOVS Sergejs
• Rok publikování: 2016
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Fuzzy Sets and Systems
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• Doi: http://dx.doi.org/10.1016/j.fss.2015.07.011
• Obor: Obecná matematika
• Klíčová slova: Bornological space; Bornological system; Bornological theory; Ideal; Powerset theory; Reflective subcategory; System spatialization procedure; Topological category; Variety of algebras

Přiložené soubory

• On_a_topological_universe_of_L-bornological_spaces_final.pdf

• Popis: 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.

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