Theorems · Theorem · general topology
nhdsWithin_mono
∀ {X : Type u} [inst : TopologicalSpace X] (x : X) {s t : Set X}, s ⊆ t → nhdsWithin x s ≤ nhdsWithin x t- Defined in
- Mathlib.Topology.Neighborhoods
- Cited by
- 82 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsproof · cited by 5,554
- nhdsWithinstatement · cited by 1,912
- Filter.principal_monoproof · cited by 30
- inf_le_inf_leftproof · cited by 25
Cited by82
Results whose statement or proof uses this declaration.
- ContinuousOn.monoproof · cited by 156
- ContinuousWithinAt.monoproof · cited by 44
- HasFDerivWithinAt.monoproof · cited by 32
- ContDiffWithinAt.compproof · cited by 18
- ContDiffWithinAt.analyticWithinAtproof · cited by 13
- nhdsGT_le_nhdsNEproof · cited by 10
- nhdsWithin_insert_of_neproof · cited by 9
- Filter.codiscreteWithin_monoproof · cited by 9
- ContDiffWithinAt.eventuallyproof · cited by 9
- nhdsLT_le_nhdsNEproof · cited by 8
- ContinuousWithinAt.preimage_mem_nhdsWithin''proof · cited by 6
- TendstoLocallyUniformlyOn.monoproof · cited by 6