Theorems · Theorem · general topology
isClosed_property2
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace β] {e : α → β} {p : β → β → Prop},
DenseRange e → IsClosed {q | p q.1 q.2} → (∀ (a₁ a₂ : α), p (e a₁) (e a₂)) → ∀ (b₁ b₂ : β), p b₁ b₂- Defined in
- Mathlib.Topology.DenseEmbedding
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.ofPredstatement and proof · cited by 6,101
- IsClosedstatement and proof · cited by 1,639
- DenseRangestatement and proof · cited by 164
- isClosed_propertyproof · cited by 13
- DenseRange.prodMapproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- DenseRange.induction_on₂proof · cited by 0