Theorems · Theorem · algebraic geometry
IsRetrocompact_iff_isSpectralMap_subtypeVal
∀ {X : Type u_2} [inst : TopologicalSpace X] {s : Set X}, IsRetrocompact s ↔ IsSpectralMap Subtype.val- Defined in
- Mathlib.Topology.Constructible
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- TopologicalSpacestatement and proof · cited by 24,529
- IsOpenproof · cited by 2,400
- IsCompactproof · cited by 1,282
- Set.inter_commproof · cited by 291
- Subtype.range_coe_subtypeproof · cited by 170
- continuous_subtype_valproof · cited by 159
- Set.image_preimage_eq_inter_rangeproof · cited by 121
- IsCompact.imageproof · cited by 105
- IsRetrocompactstatement and proof · cited by 43
- Topology.IsEmbedding.subtypeValproof · cited by 41
- Subtype.image_preimage_coeproof · cited by 37
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isRetrocompact_basicOpenproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.isConstructible_preimageproof · cited by 0