Theorems · Theorem · general topology
TopologicalSpace.Opens.isOpen
∀ {α : Type u_2} [inst : TopologicalSpace α] (U : TopologicalSpace.Opens α), IsOpen ↑U- Defined in
- Mathlib.Topology.Sets.Opens
- Cited by
- 64 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement · cited by 8,199
- IsOpenstatement · cited by 2,400
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- TopologicalSpace.Opens.is_open'proof · cited by 139
Cited by64
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.isBasis_affineOpensproof · cited by 37
- TopCat.Presheaf.germ_stalkSpecializesstatement · cited by 10
- TopCat.Presheaf.stalkSpecializes_reflproof · cited by 8
- AlgebraicGeometry.isCompact_iff_finite_and_eq_biUnion_affineOpensproof · cited by 6
- AlgebraicGeometry.Scheme.SpecMap_stalkSpecializes_fromSpecStalkproof · cited by 6
- TopCat.Presheaf.germ_stalkSpecializes_assocstatement and proof · cited by 6
- PrimeSpectrum.isOpen_basicOpenproof · cited by 5
- AlgebraicGeometry.IsAffineOpen.exists_basicOpen_leproof · cited by 5
- TopologicalSpace.Opens.isOpenEmbedding'proof · cited by 5
- TopologicalSpace.Opens.isBasis_iff_coverproof · cited by 4
- MeasureTheory.Content.innerContent_iSup_natproof · cited by 3
- AlgebraicGeometry.IsAffineOpen.isQuasiSeparatedproof · cited by 2