Theorems · Theorem · general topology
Metric.frontier_cthickening_subset
∀ {α : Type u} [inst : PseudoEMetricSpace α] (E : Set α) {δ : ℝ},
frontier (Metric.cthickening δ E) ⊆ {x | Metric.infEDist x E = ENNReal.ofReal δ}The frontier of the closed thickening of a set is contained in an Metric.infEDist level
set.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 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.
Cites12
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
- ENNRealstatement · cited by 9,879
- Set.ofPredstatement · cited by 6,101
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofRealstatement · cited by 863
- continuous_constproof · cited by 278
- frontierstatement · cited by 214
- Metric.infEDiststatement · cited by 147
- Metric.cthickeningstatement · cited by 113
- Metric.continuous_infEDistproof · cited by 9
- frontier_le_subset_eqproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Metric.frontier_cthickening_disjointproof · cited by 0