On a formula that is not in "Grothendieck Topologies in Posets"
Abstract
The paper "Grothendieck Topologies on Posets" by A.J. Lindenhovius shows that when P is an Artinian poset and E is the topos SetP then there are bijections between the set of subsets of P, the set of Grothendieck topologies on E, and the set of nuclei on the Heyting Algebra Sub(1E). It also shows that there are nice formulas for converting between subsets, Grothendieck topologies, and nuclei, but the formula for converting a nucleus to a subset is not spelled out explicitly. These notes fix that gap.
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