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No abstract

The principal application of a general theorem proved here shows that for any. choice 1 5 m 5 n 5 p of integers, there exist metric spaces X and Y such that the initial k-segments of their clones of continuous maps coincide exactly when k 5 m, are isomorphic exactly when k 5 n, and are elementarily equivalent exactly when k IP.

A category A is binding (or universal) if any full category of algebras is isomorphic to a full subcategory of A. There are many binding categories: the category of all commutative rings with unit and all unit-preserving homomorphisms [1], the category of bounded lattices [2], the category of semigroups [3], the category A(1, 1) of all algebras with two unary fundamental operations and the category of directed graphs [4], the category of all commutative groupoids [11] and many others.