Theorems · Theorem · general topology
Dense.nonempty_iff
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, Dense s → (s.Nonempty ↔ Nonempty X)- Defined in
- Mathlib.Topology.Closure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 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.
Cites7
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
- Set.Nonemptystatement and proof · cited by 2,627
- Densestatement and proof · cited by 359
- isOpen_univproof · cited by 112
- Dense.inter_open_nonemptyproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Dense.nonemptyproof · cited by 4
- DenseRange.nonempty_iffproof · cited by 2