Theorems · Theorem · general topology
IsClosed.lowerClosure_pi
∀ {ι : Type u_2} [Finite ι] {s : Set (ι → ℝ)}, IsClosed s → BddAbove s → IsClosed ↑(lowerClosure s)- Defined in
- Mathlib.Analysis.Normed.Order.UpperLower
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- SetLike.coestatement and proof · cited by 8,199
- Fintypeproof · cited by 7,736
- nhdsproof · cited by 5,554
- Set.rangeproof · cited by 4,705
- Filter.Tendstoproof · cited by 3,814
- LE.le.transproof · cited by 3,151
- Finitestatement and proof · cited by 3,029
- Filter.atTopproof · cited by 2,405
- IsClosedstatement and proof · cited by 1,639
- closureproof · cited by 1,254
Cited by2
Results whose statement or proof uses this declaration.
- IsClopen.lowerClosure_piproof · cited by 0
- closure_lowerClosure_comm_piproof · cited by 0