Theorems · Theorem · real analysis
tendsto_floor_left
∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] [inst_2 : FloorRing α] [inst_3 : TopologicalSpace α]
[IsStrictOrderedRing α] [OrderClosedTopology α] (n : ℤ),
Filter.Tendsto (fun x => ↑⌊x⌋) (nhdsWithin (↑n) (Set.Iio ↑n)) (nhdsWithin (↑n - 1) (Set.Iic (↑n - 1)))- Defined in
- Mathlib.Topology.Algebra.Order.Floor
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Filter.Tendstostatement · cited by 3,814
- IsStrictOrderedRingstatement and proof · cited by 2,490
- nhdsWithinstatement and proof · cited by 1,912
- le_rflproof · cited by 1,558
- Set.Iiostatement · cited by 1,166
- Set.Iicstatement and proof · cited by 1,111
- Filter.Tendsto.compproof · cited by 560
- OrderClosedTopologystatement and proof · cited by 445
- FloorRingstatement and proof · cited by 405
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_floor_left'proof · cited by 1