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

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