, Volume 20, Issue 3, pp 328-350

The Birkhoff Variety Theorem for continuous algebras

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Varieties of continuous algebras, i.e., classes presented by (in)equalities for terms, are characterized as precisely the HSP classes. Terms here are the usual algebraic terms enriched by iterated join symbols. A discussion of varieties which require only finitely many variables, or only the usual terms, is also presented.