Theorems · Theorem · general topology
closure_eq_compl_interior_compl
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, closure s = (interior sᶜ)ᶜ- Defined in
- Mathlib.Topology.Closure
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 62 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.
Cites12
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
- Set.ofPredproof · cited by 6,101
- Compl.complstatement and proof · cited by 2,925
- IsOpenproof · cited by 2,400
- IsClosedproof · cited by 1,639
- closurestatement and proof · cited by 1,254
- interiorstatement · cited by 714
- Set.sUnionproof · cited by 392
- Set.sInterproof · cited by 225
- Set.compl_sUnionproof · cited by 6
- Set.compl_image_ofPredproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- closure_complproof · cited by 19
- mem_closure_iff_frequentlyproof · cited by 15
- closure_unionproof · cited by 13
- interior_complproof · cited by 11
- Set.Finite.closure_biUnionproof · cited by 4
- MeasureTheory.Measure.dense_of_aeproof · cited by 1
- Filter.mem_closureproof · cited by 0