Theorems · Theorem · general topology
Ico_mem_nhdsGE
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIciTopology α] {a b : α},
b < a → Set.Ico b a ∈ nhdsWithin b (Set.Ici b)- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 8 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- 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.Icistatement and proof · cited by 1,070
- Set.Icostatement · cited by 799
- self_mem_nhdsWithinproof · cited by 215
- ClosedIciTopologystatement and proof · cited by 156
- Filter.inter_memproof · cited by 153
- nhdsWithin_le_nhdsproof · cited by 145
- Iio_mem_nhdsproof · cited by 34
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.hausdorffMeasure_zero_or_topproof · cited by 3
- continuousWithinAt_right_of_monotoneOn_of_exists_betweenproof · cited by 3
- StrictMonoOn.continuousWithinAt_right_of_exists_betweenproof · cited by 3
- Ico_mem_nhdsGE_of_memproof · cited by 2
- exists_Icc_mem_subset_of_mem_nhdsGEproof · cited by 2
- Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGEproof · cited by 2
- tendsto_floor_right_pure_floorproof · cited by 1
- Ioo_mem_nhdsGE_of_memproof · cited by 1