ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 66, 2 (1997)
pp. 243-260

CLONES IN TOPOLOGY AND ALGEBRA
J. SICHLER and V. TRNKOVA

Abstract. 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 $\caa_1$ and $\caa_2$ 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 $k\leq n_3$.

AMS subject classification. 54C05, 08A10
Keywords. Clone, clone segment, finitary algebraic theory, functors preserving finite products, categories of universal algebras

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