Theorems · Theorem · general topology
IsCompact.cthickening
∀ {α : Type u_2} [inst : PseudoMetricSpace α] [ProperSpace α] {s : Set α},
IsCompact s → ∀ {r : ℝ}, IsCompact (Metric.cthickening r s)- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpaceProperSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- PseudoMetricSpacestatement and proof · cited by 1,550
- IsCompactstatement and proof · cited by 1,282
- ProperSpacestatement and proof · cited by 190
- Metric.cthickeningstatement · cited by 113
- IsCompact.isBoundedproof · cited by 29
- Metric.isCompact_of_isClosed_isBoundedproof · cited by 8
- Metric.isClosed_cthickeningproof · cited by 5
- Bornology.IsBounded.cthickeningproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Metric.IsCover.isCompactproof · cited by 1
- ContinuousMap.dense_setOfPred_contDiffproof · cited by 1
- Complex.tendstoUniformlyOn_deriv_of_cthickening_subsetproof · cited by 1
- LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul'proof · cited by 1