Theorems · Theorem · general topology
Dense.exists_dist_lt
∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α}, Dense s → ∀ (x : α) {ε : ℝ}, 0 < ε → ∃ y ∈ s, dist x y < ε- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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
- Realstatement and proof · cited by 25,697
- Set.Nonemptyproof · cited by 2,627
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- Metric.ballproof · cited by 735
- Densestatement and proof · cited by 359
- Metric.isOpen_ballproof · cited by 63
- Dense.exists_mem_openproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- DenseRange.exists_dist_ltproof · cited by 2