Geodesic
A note on coclones of topological spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 3, pp. 403-416 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 08A68, 54H15
Keywords: clone; coclone; monoid of continuous self-maps; clone theory; monoid theory 
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Barkhudaryan, Artur. A note on coclones of topological spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 3, pp. 403-416. http://geodesic.mathdoc.fr/item/CMUC_2011_52_3_a6/