Clones of (Continuous) Partial Cofunctions
Sebastian Kerkhoff and Friedrich Martin Schneider
We introduce and study clones of partial cofunctions on sets of arbitrary cardinality.We start by outlining a general Galois theory similar to Pol-Inv. We then show some elementary results about the essential arity of clones of partial cofunctions, and take a closer look at partial idempotent cofunctions. Furthermore, we characterize all minimal clones of partial cofunctions and show that the join of all minimal clones is the full clone (provided that the Axiom of Choice is assumed). Finally, we discuss how introducing a topology and requiring the partial functions to be continuous changes the scenario.
Keywords: Clones; partial cofunctions; coclones; continuous partial functions; Galois connections; partial corelations; essential arities; minimal clones