Theorems · Theorem · general topology
nhdsWithin_singleton
∀ {α : Type u_1} [inst : TopologicalSpace α] (a : α), nhdsWithin a {a} = pure a- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 61 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 · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- nhdsproof · cited by 5,554
- nhdsWithinstatement · cited by 1,912
- inf_eq_rightproof · cited by 64
- pure_le_nhdsproof · cited by 39
- Filter.principal_singletonproof · cited by 31
Cited by12
Results whose statement or proof uses this declaration.
- nhdsWithin_insertproof · cited by 13
- Real.continuous_mul_logproof · cited by 9
- continuousOn_singletonproof · cited by 4
- nhdsNE_sup_pureproof · cited by 4
- taylor_isLittleOproof · cited by 2
- continuousWithinAt_leftLim_Iicproof · cited by 2
- exists_Icc_mem_subset_of_mem_nhdsGEproof · cited by 2
- eventuallyEq_insertproof · cited by 2
- Real.continuousAt_rpow_of_posproof · cited by 1
- exists_Icc_mem_subset_of_mem_nhdsLEproof · cited by 1
- continuousWithinAt_singletonproof · cited by 1
- tendsto_measure_Icc_nhdsWithin_rightproof · cited by 1