Theorems · Theorem · general topology
interior_union_inter_interior_compl_right_subset
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, interior (s ∪ t) ∩ interior tᶜ ⊆ interior s- Defined in
- Mathlib.Topology.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 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
- Compl.complstatement · cited by 2,925
- interiorstatement · cited by 714
- interior_monoproof · cited by 38
- interior_interproof · cited by 22
- Eq.trans_subsetproof · cited by 16
- Set.union_inter_compl_right_subsetproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- interior_union_of_disjoint_closureproof · cited by 1