Theorems · Theorem · real analysis
continuousOn_floor
∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] [inst_2 : FloorRing α] [inst_3 : TopologicalSpace α] (n : ℤ),
ContinuousOn (fun x => ↑⌊x⌋) (Set.Ico (↑n) (↑n + 1))- Defined in
- Mathlib.Topology.Algebra.Order.Floor
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- ContinuousOnstatement · cited by 1,411
- Set.Icostatement · cited by 799
- FloorRingstatement and proof · cited by 405
- Int.floorstatement · cited by 225
- continuousOn_constproof · cited by 96
- continuousOn_congrproof · cited by 5
- Int.floor_eq_on_Ico'proof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- continuousOn_fractproof · cited by 1