Theorems · Theorem · general topology
Metric.exists_eball_subset_eball
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x y : α} {ε : ENNReal},
y ∈ Metric.eball x ε → ∃ ε' > 0, Metric.eball y ε' ⊆ Metric.eball x ε- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- LT.lt.leproof · cited by 2,189
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.edistproof · cited by 735
- Eq.leproof · cited by 605
- Metric.eballstatement and proof · cited by 294
- add_tsub_cancel_of_leproof · cited by 79
- ne_top_of_ltproof · cited by 50
- Metric.mem_eballproof · cited by 18
- Metric.eball_subsetproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Metric.isOpen_eballproof · cited by 13
- EMetric.exists_ball_subset_ballproof · cited by 0