Theorems · Theorem · general topology
interior_compl
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, interior sᶜ = (closure s)ᶜ- Defined in
- Mathlib.Topology.Closure
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 63 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.
Cites7
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
- Compl.complstatement and proof · cited by 2,925
- closurestatement · cited by 1,254
- interiorstatement and proof · cited by 714
- compl_complproof · cited by 229
- closure_eq_compl_interior_complproof · cited by 7
Cited by11
Results whose statement or proof uses this declaration.
- interior_Ici'proof · cited by 13
- regularSpace_TFAEproof · cited by 6
- upperHemicontinuousWithinAt_iff_frequentlyproof · cited by 3
- disjoint_principal_nhdsSetproof · cited by 2
- Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGEproof · cited by 2
- interior_union_of_disjoint_closureproof · cited by 1
- DenseRange.zpow_of_ergodic_mul_leftproof · cited by 1
- DenseRange.zsmul_of_ergodic_add_leftproof · cited by 1
- isClosedMap_iff_kernImage_interiorproof · cited by 0
- isOpenMap_iff_closure_kernImageproof · cited by 0
- Set.ordT5Nhd_mem_nhdsSetproof · cited by 0