Theorems · Theorem · general topology
IsClosed.stableUnderSpecialization
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, IsClosed s → StableUnderSpecialization s- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 77 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.
Cites6
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
- IsClosedstatement and proof · cited by 1,639
- Specializesproof · cited by 176
- StableUnderSpecializationstatement · cited by 32
- Specializes.mem_closedproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- IsClosedMap.specializingMapproof · cited by 2
- stableUnderSpecialization_iff_exists_sUnion_eqproof · cited by 1
- PrimeSpectrum.closure_image_comap_zeroLocusproof · cited by 1
- AlgebraicGeometry.isClosedMap_iff_specializingMapproof · cited by 1
- specializingMap_iff_isClosed_image_closure_singletonproof · cited by 0
- PrimeSpectrum.stableUnderSpecialization_image_iffproof · cited by 0
- PrimeSpectrum.stableUnderSpecialization_range_iffproof · cited by 0
- PrimeSpectrum.isQuotientMap_of_specializingMapproof · cited by 0