Theorems · Theorem · general topology
IsOpen.subset_interior_closure
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsOpen s → s ⊆ interior (closure s)- Defined in
- Mathlib.Topology.Closure
- Cited by
- 3 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
- IsOpenstatement and proof · cited by 2,400
- closurestatement · cited by 1,254
- interiorstatement · cited by 714
- subset_closureproof · cited by 309
- IsOpen.subset_interior_iffproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- closure_interior_idemproof · cited by 0
- interior_closure_idemproof · cited by 0
- Disjoint.hasSeparatingCover_closed_gdelta_rightproof · cited by 0