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Keywords:
clone; coclone; monoid of continuous self-maps; clone theory; monoid theory
clone; coclone; monoid of continuous self-maps; clone theory; monoid theory
Summary:
The clone of a topological space is known to have a strictly more expressive first-order language than that of the monoid of continuous self-maps. The current paper studies coclones of topological spaces (i.e. clones in the category dual to that of topological spaces and continuous maps) and proves that, in contrast to clones, the first-order properties of coclones cannot express anything more than those of the monoid, except for the case of discrete and indiscrete spaces.
References:
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