Theorems · Theorem · general topology
pi_Ico_mem_nhds
∀ {ι : Type u_1} {X : ι → Type u_2} [Finite ι] [inst : (i : ι) → LinearOrder (X i)]
[inst_1 : (i : ι) → TopologicalSpace (X i)] [∀ (i : ι), OrderTopology (X i)] {a b x : (i : ι) → X i} [Nonempty ι],
(∀ (i : ι), x i < a i) → (∀ (i : ι), b i < x i) → Set.Ico b a ∈ nhds x- Defined in
- Mathlib.Topology.Order.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Set.univproof · cited by 3,945
- Finitestatement and proof · cited by 3,029
- OrderTopologystatement and proof · cited by 1,355
- Set.Icostatement · cited by 799
- Filter.mem_of_supersetproof · cited by 308
- Set.finite_univproof · cited by 52
- set_pi_mem_nhdsproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- pi_Ico_mem_nhds'proof · cited by 0