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On A Formula That Is Not In Grothendieck Topologies In Posets'.pdf

2021lindenhovius-j-to-X.pdf

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Bert Lindenhovius shows that when P is Artinian, there are bijections between P(P), Nucs(P), and GrTops(P), with components denoted as (j 7→J), (J 7→j), (X 7→j), (j 7→X), (X 7→J), and (J 7→X). The notes prove that Xj = XJj, where Xj = {p ∈ P : p ∉ j(↓p\{p})} and XJj = {p ∈ P : ∀S ∈ D(↓p). (p ∈ j(S)) ⇔ (S = ↓p)}, and also that Xj = X′j, where X′j = {p ∈ P : j(↓p) ≠ j(↓p\{p})}.

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Bert Lindenhovius shows that when P is Artinian, there are bijections between P(P), Nucs(P), and GrTops(P), with components denoted as (j 7→J), (J 7→j), (X...

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File Format: PDF
File Size: 122 KB
Pages: 4
Language: EN
Total Downloads: 55
Last Updated: 1 week ago

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