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arXiv · 1809.04124

Categorical foundations of variety-based bornology

Jan Paseka·Sergey A. Solovyov
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Abstract

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.

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Jan Paseka, Sergey A. Solovyov. 2018-09-11. Categorical foundations of variety-based bornology. https://doi.org/10.1016/j.fss.2015.07.011

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