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August 21, 2013 / porton

Changed the definition of order of pointfree funcoids

In my preprint I defined pre-order of pointfree funcoids by the formula f\sqsubseteq g \Leftrightarrow [f]\subseteq[g]. Sadly this does not define a poset, but only a pre-order.

Recently I’ve found an other (non-equivalent) definition of an order on pointfree funcoids, this time this is a partial order not just a pre-order:

f \sqsubseteq g \Leftrightarrow \forall x \in \mathfrak{A}: \langle f \rangle  x \sqsubseteq \langle g \rangle x \wedge \forall y \in \mathfrak{B}: \langle  f^{- 1} \rangle y \sqsubseteq \langle g^{- 1} \rangle y.

I will systematically rewrite the relevant chapters of my manuscript to replace the old definition with the new one.


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