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Varieties of topological algebras. (English. Russian original) Zbl 0572.08006

Sib. Math. J. 25, 783-790 (1984); translation from Sib. Mat. Zh. 25, No. 5(147), 125-134 (1984).
The author studies a theory of varieties of topological algebras. Here a topological algebra is a universal algebra equipped with a topology so that the (finitary) algebra operations are continuous. The paper is rather technical and intended for the specialists. The titles of sections are: Algebra of filters; Identities in topological algebras; Free topological algebras; Varieties, classification and characterization; Rank of a variety and a-products; Remarks on varieties of topological spaces.
Reviewer: W.Żelazko

MSC:

08B20 Free algebras
22A30 Other topological algebraic systems and their representations
54A05 Topological spaces and generalizations (closure spaces, etc.)
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
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References:

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