Theorems · Theorem · general topology
nhdsWithin_Ioo_eq_nhdsGT
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIciTopology α] {a b : α},
b < a → nhdsWithin b (Set.Ioo b a) = nhdsWithin b (Set.Ioi b)- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 9 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
- Filterstatement · cited by 8,121
- nhdsWithinstatement and proof · cited by 1,912
- Set.Ioistatement and proof · cited by 1,463
- Set.Ioostatement · cited by 1,214
- ClosedIciTopologystatement and proof · cited by 156
- nhdsWithin_le_nhdsproof · cited by 145
- Iio_mem_nhdsproof · cited by 34
- nhdsWithin_inter_of_memproof · cited by 20
Cited by9
Results whose statement or proof uses this declaration.
- HasDerivAt.lhopital_zero_right_on_Iooproof · cited by 5
- MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAtproof · cited by 3
- TFAE_mem_nhdsGTproof · cited by 3
- eq_lim_at_left_extendFrom_Iooproof · cited by 1
- continuousOn_uIcc_extendFrom_uIooproof · cited by 1
- continuousOn_Ico_extendFrom_Iooproof · cited by 1
- deriv.lhopital_zero_right_on_Icoproof · cited by 0
- HasDerivAt.lhopital_zero_right_on_Icoproof · cited by 0
- continuousWithinAt_Ioo_iff_Ioiproof · cited by 0