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Closure operators. I. (English) Zbl 0634.54008
Closure operators form a familiar tool in topology. The authors introduce an abstract notion of closure operator in the realm of arbitrary categories. It turns out that there is a close connection between closure operators and factorization structures (for sinks). In particular for suitable categories there is a Galois equivalence (a) between idempotent, weakly hereditary closure operators and factorization systems, (b) between regular closure operators and strongly epireflective subcategories, and (c) between standard closure operators and preradicals. The paper ends with a discussion of several highly interesting examples in abelian categories, in universal algebras, and in topology.
Reviewer: H.Herrlich

MSC:
54B30 Categorical methods in general topology
18A32 Factorization systems, substructures, quotient structures, congruences, amalgams
18B30 Categories of topological spaces and continuous mappings (MSC2010)
18E40 Torsion theories, radicals
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