Algebras with a compatible uniformity

Details Algebras with a compatible uniformity Algebras with a compatible uniformity

2000-05-16

arxiv.org/abs/math/0005153v2

Mathematics

Rings and Algebras

28 pages; minor revisions

Scientific paper

Given a variety of algebras V, we study categories of algebras in V with a compatible structure of uniform space. The lattice of compatible uniformities of an algebra, Unif A, can be considered a generalization of the lattice of congruences Con A. Mal'cev properties of V influence the structure of Unif A, much as they do that of Con A. The category V[CHUnif] of complete, Hausdorff uniform algebras in the variety V is particularly interesting; it has a natural factorization system extending the usual (onto, one-one) factorization system of V.

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