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Clones in topology and algebra. (English) Zbl 0970.08004
Summary: Clones of continuous maps of topological spaces and clones of homomorphisms of universal algebras are investigated and their initial segments compared. We show, for instance, that for every triple \(2\leq n_1 \leq n_2 \leq n_3\) of integers there exist algebras \(\mathcal A_1\) and \(\mathcal A_2\) with two unary operations such that the initial \(k\)-segments of their clones of homomorphisms are equal exactly when \(k \leq n_1\), isomorphic exactly when \(k \leq n_2\) and elementarily equivalent exactly when \(k \leq n_3\).

MSC:
08A40 Operations and polynomials in algebraic structures, primal algebras
54C05 Continuous maps
08C05 Categories of algebras
08A05 Structure theory of algebraic structures
08A62 Finitary algebras
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