Theorems · Theorem · general topology
nhdsWithin_univ
∀ {α : Type u_1} [inst : TopologicalSpace α] (a : α), nhdsWithin a Set.univ = nhds a- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 88 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Set.univstatement and proof · cited by 3,945
- nhdsWithinstatement · cited by 1,912
- Filter.principal_univproof · cited by 46
- inf_top_eqproof · cited by 30
Cited by88
Results whose statement or proof uses this declaration.
- nhdsWithin_le_nhdsproof · cited by 145
- continuousOn_univproof · cited by 43
- continuousWithinAt_univproof · cited by 22
- hasFDerivWithinAt_univproof · cited by 14
- tendstoLocallyUniformlyOn_univproof · cited by 10
- HasFDerivAt.uniqueproof · cited by 9
- Real.continuous_mul_logproof · cited by 9
- MeasureTheory.locallyIntegrableOn_univproof · cited by 7
- HasFPowerSeriesAt.hasStrictFDerivAtproof · cited by 7
- ContDiffAt.eventuallyproof · cited by 7
- Metric.tendsto_nhdsWithin_nhdsproof · cited by 6
- nhds_bot_basisproof · cited by 6