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April 21, 2010 / porton

A counterexample against “Meet of discrete funcoids is discrete”

I found a counterexample to the following conjecture:

Conjecture f\cap^{\mathsf{FCD}} g = f\cap g for every binary relations f and g.

The counter-example is f = {(=)}|_{\mho} and g = \mho\times\mho \setminus f. I proved f \cap^{\mathsf{FCD}} g = {(=)} |_{\Omega} (where \Omega is the Frechet filter object).

The proof of this equality is presented in Funcoids and Reloids online article, the section Some counter-examples.

I hope the above counter-example may probably serve also as a base for disproving some conjectures about relationships of funcoids and reloids.

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