Theorems · Theorem · general topology
ContractingWith.edist_efixedPoint_lt_top
∀ {α : Type u_1} [inst : EMetricSpace α] {K : NNReal} {f : α → α} [inst_1 : CompleteSpace α] (hf : ContractingWith K f)
{x : α} (hx : edist x (f x) ≠ ⊤), edist x (ContractingWith.efixedPoint f hf x hx) < ⊤- Defined in
- Mathlib.Topology.MetricSpace.Contracting
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EMetricSpaceCompleteSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- NNRealstatement and proof · cited by 4,310
- CompleteSpacestatement and proof · cited by 2,532
- LE.le.trans_ltproof · cited by 795
- EDist.ediststatement and proof · cited by 735
- EMetricSpacestatement and proof · cited by 242
- Ne.lt_topproof · cited by 161
- ENNReal.mul_ne_topproof · cited by 41
- ContractingWithstatement and proof · cited by 39
- ENNReal.inv_ne_topproof · cited by 12
- ContractingWith.efixedPointstatement · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- ContractingWith.efixedPoint_eq_of_edist_lt_topproof · cited by 0