Theorems · Theorem · real analysis
tendsto_ceil_left_pure_ceil
∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] [inst_2 : FloorRing α] [inst_3 : TopologicalSpace α]
[IsStrictOrderedRing α] [OrderClosedTopology α] (x : α), Filter.Tendsto Int.ceil (nhdsWithin x (Set.Iic x)) (pure ⌈x⌉)- Defined in
- Mathlib.Topology.Algebra.Order.Floor
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Filterstatement · cited by 8,121
- Ringstatement and proof · cited by 7,463
- Filter.Tendstostatement · cited by 3,814
- LE.le.transproof · cited by 3,151
- IsStrictOrderedRingstatement and proof · cited by 2,490
- nhdsWithinstatement · cited by 1,912
- Set.Iicstatement · cited by 1,111
- Set.Iocproof · cited by 971
- OrderClosedTopologystatement and proof · cited by 445
- FloorRingstatement and proof · cited by 405
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_ceil_left_pureproof · cited by 1