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Approximation in compact topological universal algebras. (English) Zbl 0695.08011
General algebra, Dedicated Mem. of Wilfried Nöbauer, Contrib. Gen. Algebra 6, 117-122 (1988).
Summary: [For the entire collection see Zbl 0694.00002.]
Interpolation in universal algebras has been recently investigated thoroughly. As a next logical step G. Kowohl [Monatsh. Math. 93, 15-32 (1982; Zbl 0468.08006), J. Algebra 86, 1-13 (1984; Zbl 0545.08004)] studied the approximation property in topological universal algebras. The problem of describing all topological universal algebras possessing the approximation property in given classes of algebras has been solved by G. Kowol in a number of important cases such as: topological lattices, topological groups, topological loops, topological rings and topological near-rings. The aim of this paper is to give a general characterization of compact topological universal algebras having the approximation property. From this theorem G. Kowol’s results can easily be deduced if the topological universal algebras under consideration satisfy the additional property of compactness.
MSC:
08A40 Operations and polynomials in algebraic structures, primal algebras
22A30 Other topological algebraic systems and their representations