Theorems · Theorem · general topology
interior_subset_closure
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, interior s ⊆ closure s- 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.
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
- closurestatement · cited by 1,254
- interiorstatement · cited by 714
- subset_closureproof · cited by 309
- Set.Subset.transproof · cited by 218
- interior_subsetproof · cited by 171
Cited by7
Results whose statement or proof uses this declaration.
- Convex.interiorproof · cited by 14
- closure_eq_interior_union_frontierproof · cited by 4
- closure_sdiff_frontierproof · cited by 2
- Convex.addHaar_frontierproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOneproof · cited by 1
- Complex.exists_mem_frontier_isMaxOn_normproof · cited by 1