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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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