Theorems · Theorem · general topology
nhdsSet_singleton
∀ {X : Type u_2} [inst : TopologicalSpace X] {x : X}, nhdsSet {x} = nhds x- Defined in
- Mathlib.Topology.NhdsSet
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 51 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.
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 · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- SupSet.sSupproof · cited by 954
- nhdsSetstatement · cited by 267
- Set.image_singletonproof · cited by 174
- sSup_singletonproof · cited by 14
Cited by19
Results whose statement or proof uses this declaration.
- principal_nhdsKer_singletonproof · cited by 4
- nhdsSet_insertproof · cited by 4
- isClosedMap_iff_comap_nhds_leproof · cited by 3
- nhdsKer_singleton_eq_ker_nhdsproof · cited by 3
- Continuous.tendsto_nhdsSet_nhdsproof · cited by 2
- upperHemicontinuousWithinAt_singleton_iffproof · cited by 2
- exists_mem_nhds_isCompact_mapsTo_of_isCompact_mem_nhdsproof · cited by 1
- upperHemicontinuous_singleton_idproof · cited by 1
- nhds_prod_le_of_disjoint_cocompactproof · cited by 1
- IsCompact.le_nhds_of_unique_clusterPtproof · cited by 1
- prod_nhds_le_of_disjoint_cocompactproof · cited by 1
- nhdsSetWithin_singletonproof · cited by 0