Theorems · Theorem · real analysis
continuousOn_ceil
∀ {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.Ioc (↑n - 1) ↑n)- Defined in
- Mathlib.Topology.Algebra.Order.Floor
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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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.Iocstatement · cited by 971
- FloorRingstatement and proof · cited by 405
- Int.ceilstatement · cited by 138
- continuousOn_constproof · cited by 96
- continuousOn_congrproof · cited by 5
- Int.ceil_eq_on_Ioc'proof · cited by 1
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