Theorems · Theorem · general topology
Metric.isClosedEmbedding_of_pairwise_le_dist
∀ {γ : Type w} [inst : MetricSpace γ] {α : Type u_2} [inst_1 : TopologicalSpace α] [DiscreteTopology α] {ε : ℝ},
0 < ε → ∀ {f : α → γ}, (Pairwise fun x y => ε ≤ dist (f x) (f y)) → Topology.IsClosedEmbedding f- Defined in
- Mathlib.Topology.MetricSpace.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
- Pairwisestatement and proof · cited by 516
- DiscreteTopologystatement and proof · cited by 373
- Topology.IsClosedEmbeddingstatement · cited by 195
- Metric.dist_mem_uniformityproof · cited by 23
- isClosedEmbedding_of_spaced_outproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Int.isClosedEmbedding_coe_realproof · cited by 3
- Nat.isClosedEmbedding_coe_realproof · cited by 2
- Nat.isClosedEmbedding_coe_ratproof · cited by 0
- Int.isClosedEmbedding_coe_ratproof · cited by 0
- NormedSpace.noncompactSpaceproof · cited by 0