Theorems · Theorem · general topology
isOpen_interior
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsOpen (interior s)- Defined in
- Mathlib.Topology.Closure
- Cited by
- 130 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 21 definitions · 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsOpenstatement · cited by 2,400
- interiorstatement · cited by 714
- isOpen_sUnionproof · cited by 15
Cited by132
Results whose statement or proof uses this declaration.
- OpenPartialHomeomorph.restrproof · cited by 47
- interior_monoproof · cited by 38
- interior_interproof · cited by 22
- preimage_interior_subset_interior_preimageproof · cited by 14
- uniformity_hasBasis_openproof · cited by 10
- interior_interiorproof · cited by 8
- TendstoLocallyUniformlyOn.differentiableOnproof · cited by 7
- interior_mem_nhdsproof · cited by 7
- uniformContinuous_uniformly_extendproof · cited by 6
- ContDiffWithinAt.isSymmSndFDerivWithinAtproof · cited by 6
- interior_eq_iff_isOpenproof · cited by 6
- TopologicalSpace.Opens.interiorproof · cited by 6