I’ve found an easy positive proof of this my conjecture.

read moreConjecture $latex S^{\ast}(\mu(E)) = E$ for every partial order $latex E$. The function $latex S^\ast$ and micronization $latex \mu$ are defined in my research monograph.

read moreI’ve added the following to my research book: Definition Galois surjection is the special case of Galois connection such that $latex f^{\ast} \circ f_{\ast} $ is identity. Proposition For Galois surjection $latex \mathfrak{A} \rightarrow \mathfrak{B}$ such that $latex \mathfrak{A}$ is a join-semilattice…

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