Theorems · Theorem · general topology
IsOpen.nhdsWithin_eq
∀ {α : Type u_1} [inst : TopologicalSpace α] {a : α} {s : Set α}, IsOpen s → a ∈ s → nhdsWithin a s = nhds a- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- nhdsstatement · cited by 5,554
- IsOpenstatement and proof · cited by 2,400
- nhdsWithinstatement · cited by 1,912
- IsOpen.mem_nhdsproof · cited by 470
- nhdsWithin_eq_nhdsproof · cited by 8
Cited by15
Results whose statement or proof uses this declaration.
- Ne.nhdsWithin_compl_singletonproof · cited by 4
- ConvexOn.continuousOn_tfaeproof · cited by 3
- hasDerivAt_of_tendstoLocallyUniformlyOnproof · cited by 3
- hasFDerivAt_of_tendstoLocallyUniformlyOnproof · cited by 2
- IsOpen.tendstoLocallyUniformlyOn_iff_forall_tendstoproof · cited by 2
- eVariationOn.eVariationOn_leftLim_leproof · cited by 1
- eVariationOn.eVariationOn_rightLim_leproof · cited by 1
- MeasureTheory.Measure.support_mem_ae_of_isLindelofproof · cited by 1
- isMIntegralCurveOn_piecewiseproof · cited by 1
- OpenPartialHomeomorph.nhds_eq_comap_inf_principalproof · cited by 1
- eventually_nhdsWithin_eventually_nhds_iff_of_isOpenproof · cited by 1
- IsDiscrete.image_of_isOpenMap_of_isOpenproof · cited by 1