Theorems · Theorem · general topology
IsOpen.stableUnderGeneralization
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, IsOpen s → StableUnderGeneralization s- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 6 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
- IsOpenstatement and proof · cited by 2,400
- Specializesproof · cited by 176
- Specializes.mem_openproof · cited by 27
- StableUnderGeneralizationstatement · cited by 24
Cited by6
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isOpenMap_comap_of_hasGoingDown_of_finitePresentationproof · cited by 2
- PrimeSpectrum.isOpen_singleton_tfae_of_isNoetherian_of_isJacobsonRingproof · cited by 2
- PrimeSpectrum.isQuotientMap_of_generalizingMapproof · cited by 1
- Topology.IsOpenEmbedding.generalizingMapproof · cited by 1
- TopologicalSpace.IsOpenCover.generalizingMap_iff_restrictPreimageproof · cited by 0
- stableUnderGeneralization_iff_exists_sInter_eqproof · cited by 0