Theorems · Theorem · general topology
closure_sdiff_frontier
∀ {X : Type u} [inst : TopologicalSpace X] (s : Set X), closure s \ frontier s = interior s- Defined in
- Mathlib.Topology.Closure
- Cited by
- 2 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.
Cites8
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 and proof · cited by 1,254
- interiorstatement and proof · cited by 714
- frontierstatement · cited by 214
- Set.inter_eq_self_of_subset_rightproof · cited by 39
- interior_subset_closureproof · cited by 7
- Set.sdiff_sdiff_right_selfproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- intrinsicClosure_sdiff_intrinsicFrontierproof · cited by 2
- closure_diff_frontierproof · cited by 0