Theorems · Theorem · general topology
IsClosed.closure_interior_subset
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsClosed s → closure (interior s) ⊆ 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
- IsClosedstatement and proof · cited by 1,639
- closurestatement · cited by 1,254
- interiorstatement · cited by 714
- interior_subsetproof · cited by 171
- IsClosed.closure_subset_iffproof · cited by 59
Cited by3
Results whose statement or proof uses this declaration.
- closure_interior_idemproof · cited by 0
- ModelWithCorners.range_eq_closure_interiorproof · cited by 0
- interior_closure_idemproof · cited by 0