Theorems · Theorem · general topology
Subtype.dense_iff
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X} {t : Set ↑s}, Dense t ↔ s ⊆ closure (Subtype.val '' t)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 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.Elemstatement and proof · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- closurestatement and proof · cited by 1,254
- Densestatement · cited by 359
- Topology.IsInducing.subtypeValproof · cited by 43
- SetCoe.forallproof · cited by 10
- Topology.IsInducing.dense_iffproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- TopologicalSpace.IsSeparable.secondCountableTopologyproof · cited by 4
- denseRange_inclusion_iffproof · cited by 1
- IsGδ.baireSpace_of_denseproof · cited by 1