Theorems · Theorem · general topology
coborder_inter_closure
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, coborder s ∩ closure s = s- Defined in
- Mathlib.Topology.LocallyClosed
- Cited by
- 2 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.
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
- subset_closureproof · cited by 309
- Set.inter_eq_rightproof · cited by 41
- coborderstatement · cited by 22
- Set.sdiff_eq_compl_interproof · cited by 17
- Set.sdiff_sdiff_right_selfproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- isClosed_preimage_val_coborderproof · cited by 1
- closure_inter_coborderproof · cited by 1