Theorems · Theorem · general topology
isClosedEmbedding_of_spaced_out
∀ {β : Type v} [inst : UniformSpace β] {α : Type u_1} [inst_1 : TopologicalSpace α] [DiscreteTopology α] [T0Space β]
{f : α → β} {s : Set (β × β)}, s ∈ uniformity β → (Pairwise fun x y => (f x, f y) ∉ s) → Topology.IsClosedEmbedding f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Filterstatement · cited by 8,121
- Bot.botproof · cited by 4,720
- UniformSpacestatement and proof · cited by 2,040
- uniformitystatement and proof · cited by 765
- Pairwisestatement and proof · cited by 516
- DiscreteTopologystatement and proof · cited by 373
- Topology.IsEmbeddingproof · cited by 294
- Topology.IsClosedEmbeddingstatement · cited by 195
- T0Spacestatement and proof · cited by 179
- IsUniformEmbedding.isEmbeddingproof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- Metric.isClosedEmbedding_of_pairwise_le_distproof · cited by 5