Theorems · Theorem · real analysis
continuousAt_fract
∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] [inst_2 : FloorRing α] [inst_3 : TopologicalSpace α]
[OrderClosedTopology α] [IsTopologicalAddGroup α] {x : α}, x ≠ ↑⌊x⌋ → ContinuousAt Int.fract x- Defined in
- Mathlib.Topology.Algebra.Order.Floor
- 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.
Cites15
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
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- ContinuousAtstatement · cited by 697
- OrderClosedTopologystatement and proof · cited by 445
- FloorRingstatement and proof · cited by 405
- Int.floorstatement and proof · cited by 225
- LE.le.lt_of_neproof · cited by 116
- Int.fractstatement · cited by 114
- ContinuousOn.continuousAtproof · cited by 33
- Int.floor_leproof · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousOn.comp_fract'proof · cited by 1