Dualizing clones into categories of topological spaces

摘要

In this paper, we study clones of dual operations in the category of topological spaces. Our investigation is motivated by the possibility to apply duality theory in order to obtain some information about clones in the classical sense. In this way, we deduce results about the centralizer clones of (not necessarily finite) Boolean algebras, C~?-algebras and bounded distributive lattices. We examine their arity sequences, discuss the structure of the lattices given by their subclones, and take a closer look at their idempotent operations.