Theorems · Theorem · general topology
frontier_interior_subset
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, frontier (interior s) ⊆ frontier s- Defined in
- Mathlib.Topology.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 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.
Cites9
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
- interiorstatement · cited by 714
- frontierstatement · cited by 214
- interior_subsetproof · cited by 171
- closure_monoproof · cited by 133
- Eq.subsetproof · cited by 124
- Set.sdiff_subset_sdiffproof · cited by 11
- interior_interiorproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Complex.exists_mem_frontier_isMaxOn_normproof · cited by 1