Publication detail

Categorical foundations of variety-based bornology

Paseka Jan, Solovjovs Sergejs

English title

Categorical foundations of variety-based bornology

Type

journal article in Web of Science

Language

en

Original 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.

English 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.

Keywords in English

Bornological space; Bornological system; Bornological theory; Ideal; Powerset theory; Reflective subcategory; System spatialization procedure; Topological category; Variety of algebras

Released

01.05.2016

Publisher

ELSEVIER SCIENCE BV

Location

NETHERLANDS

ISSN

0165-0114

Volume

291

Number

1

Pages from–to

132–143

Pages count

11

BIBTEX


@article{BUT126462,
  author="Sergejs {Solovjovs},
  title="Categorical foundations of variety-based bornology",
  year="2016",
  volume="291",
  number="1",
  month="May",
  pages="132--143",
  publisher="ELSEVIER SCIENCE BV",
  address="NETHERLANDS",
  issn="0165-0114"
}