Theorems · Theorem · general topology
interior_eq_empty_iff_dense_compl
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, interior s = ∅ ↔ Dense sᶜ- Defined in
- Mathlib.Topology.Closure
- Cited by
- 5 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.
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
- Set.univproof · cited by 3,945
- Compl.complstatement · cited by 2,925
- interiorstatement and proof · cited by 714
- Densestatement · cited by 359
- dense_iff_closure_eqproof · cited by 26
- closure_complproof · cited by 19
- Set.compl_univ_iffproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- interior_singletonproof · cited by 2
- Set.Countable.dense_complproof · cited by 1
- Dense.interior_complproof · cited by 1
- Rat.dense_compl_compactproof · cited by 0
- isClosed_isNowhereDense_iff_complproof · cited by 0