Theorems · Theorem · general topology
interior_eq_univ
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, interior s = Set.univ ↔ s = Set.univ- 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
- Set.univstatement and proof · cited by 3,945
- interiorstatement and proof · cited by 714
- interior_subsetproof · cited by 171
- Eq.trans_leproof · cited by 155
- Set.univ_subset_iffproof · cited by 49
- interior_univproof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.continuous_mgfproof · cited by 1