Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_basicOpen
∀ {X : AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsAffine X] {U : Set ↥X},
IsCompact U ∧ IsOpen U ↔ ∃ s, s.Finite ∧ U = ⋃ i ∈ s, ↑(X.basicOpen i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AlgebraicGeometry.IsAffine
Around this declaration
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Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement · cited by 8,199
- Oppositestatement · cited by 8,081
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- Set.iUnionstatement · cited by 2,483
- IsOpenstatement · cited by 2,400
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
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