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Clone segment independence in topology and algebra. (English) Zbl 1017.54006
Summary: This a complete characterization of all possible simultaneous relations between the clones of uniformly continuous maps of two metric spaces and the respective clones of their continuous maps in terms of the equality, isomorphism and elementary equivalence of their initial clone segments. In conjunction with earlier results, the apparatus introduced here gives a full characterization of the equality, isomorphism and elementary equivalence of clone segments for two topological spaces and their various lower and upper modifications, and a similar characterization of the segments of centralizer clones for two algebras with at least three non-nullary operations and their respective reducts.

MSC:
54C05 Continuous maps
08C05 Categories of algebras
08A40 Operations and polynomials in algebraic structures, primal algebras
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