Theorems · Theorem · general topology
IsClopen.of_thickening_subset_self
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s : Set α} {δ : ℝ}, 0 < δ → Metric.thickening δ s ⊆ s → IsClopen s- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 156 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
- le_antisymmproof · cited by 2,068
- PseudoEMetricSpacestatement and proof · cited by 1,536
- LE.le.trans_eqproof · cited by 328
- IsClopenstatement · cited by 189
- Metric.thickeningstatement and proof · cited by 130
- Set.iInter₂_subsetproof · cited by 15
- Metric.isOpen_thickeningproof · cited by 11
- closure_subset_iff_isClosedproof · cited by 11
- Metric.self_subset_thickeningproof · cited by 10
- Metric.closure_eq_iInter_thickeningproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Unitary.mem_pathComponentOne_iffproof · cited by 0
- IsClopen.of_cthickening_subset_selfproof · cited by 0