Theorems · Theorem · general topology
IsLowerSet.exists_subset_ball
∀ {ι : Type u_2} [inst : Fintype ι] {s : Set (ι → ℝ)} {x : ι → ℝ} {δ : ℝ},
IsLowerSet s →
x ∈ closure s →
0 < δ → ∃ y, Metric.closedBall y (δ / 4) ⊆ Metric.closedBall x δ ∧ Metric.closedBall y (δ / 4) ⊆ interior s- Defined in
- Mathlib.Analysis.Normed.Order.UpperLower
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
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
- Fintypestatement and proof · cited by 7,736
- Norm.normproof · cited by 5,413
- LE.le.transproof · cited by 3,151
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- Dist.distproof · cited by 1,539
- closurestatement and proof · cited by 1,254
- interiorstatement · cited by 714
Cited by2
Results whose statement or proof uses this declaration.
- IsLowerSet.null_frontierproof · cited by 1
- IsUpperSet.null_frontierproof · cited by 1