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I have added to my free ebook a definition of $T_4$-funcoids (generalizing $T_4$ topologies).

A funcoid $f$ is $T_4$ iff $f \circ f^{- 1} \circ f \circ f^{- 1} \sqsubseteq f \circ f^{- 1}$. This can also be generalized for pointfree funcoids.

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