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### Can lattice join be an element of residuated pair?

Given a classic (not Residuated) lattice, with standard definition of partial order via lattice join and meet operations, is it possible to satisfy Galois equivalence
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### When does a Galois connection induce a topology?

Let $(X,\leq)$ and $(Y,\leq)$ by partially ordered sets. Recall that a(n antitone) Galois connection between $X$ and $Y$ is a pair of order-reversing maps
$\Phi: X \rightarrow Y, \ \Psi: Y ...