Theorems · Theorem · general topology
Metric.cthickening_zero
∀ {α : Type u} [inst : PseudoEMetricSpace α] (E : Set α), Metric.cthickening 0 E = closure EThe closed thickening with radius zero is the closure of the set.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 153 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.
Cites7
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 · cited by 25,697
- le_rflproof · cited by 1,558
- PseudoEMetricSpacestatement and proof · cited by 1,536
- closurestatement · cited by 1,254
- Metric.cthickeningstatement · cited by 113
- Metric.cthickening_of_nonposproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- Metric.closure_eq_iInter_thickeningproof · cited by 3
- Metric.closure_subset_thickeningproof · cited by 3
- closure_thickeningproof · cited by 2
- Metric.closure_eq_iInter_cthickeningproof · cited by 1
- thickening_cthickeningproof · cited by 1
- blimsup_cthickening_ae_le_of_eventually_mul_le_auxproof · cited by 1
- Metric.closure_eq_iInter_cthickening'proof · cited by 0
- Metric.closure_eq_iInter_thickening'proof · cited by 0