Theorems · Theorem · general topology
Metric.continuous_infNndist_pt
∀ {α : Type u} [inst : PseudoMetricSpace α] (s : Set α), Continuous fun x => Metric.infNndist x sThe minimal distance to a set (as ℝ≥0) is continuous in point
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 158 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.
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
- NNRealstatement · cited by 4,310
- Continuousstatement · cited by 2,592
- PseudoMetricSpacestatement and proof · cited by 1,550
- UniformContinuous.continuousproof · cited by 66
- Metric.infNndiststatement · cited by 8
- Metric.uniformContinuous_infNndist_ptproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- measurable_of_tendsto_metrizable'proof · cited by 7
- measurable_infNndistproof · cited by 1