Theorems · Theorem · general topology
map_coe_Ioi_atBot
∀ {X : Type u_1} [inst : LinearOrder X] [inst_1 : TopologicalSpace X] [OrderTopology X] (a : X),
autoParam (Order.IsPredPrelimit a) map_coe_Ioi_atBot._auto_1 →
Filter.map Subtype.val Filter.atBot = nhdsWithin a (Set.Ioi a)- Defined in
- Mathlib.Topology.Order.AtTopBotIxx
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 · cited by 1,912
- Set.Ioistatement · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- Filter.mapstatement · cited by 819
- Filter.atBotstatement · cited by 512
- Set.Subset.rflproof · cited by 255
- Order.IsPredPrelimitstatement and proof · cited by 93
- Set.Ioo_subset_Ioi_selfproof · cited by 20
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.tendsto_measure_biInter_gtproof · cited by 3
- Real.map_exp_atBotproof · cited by 2
- map_coe_Iio_atTopproof · cited by 1
- tendsto_comp_coe_Ioi_atBotproof · cited by 1