Theorems · Theorem · general topology
mem_closure_iff_nhdsWithin_neBot
∀ {X : Type u} [inst : TopologicalSpace X] {x : X} {s : Set X}, x ∈ closure s ↔ (nhdsWithin x s).NeBot- Defined in
- Mathlib.Topology.ClusterPt
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 74 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.
Cites6
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
- nhdsWithinstatement · cited by 1,912
- closurestatement · cited by 1,254
- Filter.NeBotstatement · cited by 853
- mem_closure_iff_clusterPtproof · cited by 16
Cited by16
Results whose statement or proof uses this declaration.
- dense_compl_singletonproof · cited by 6
- IsLUB.nhdsWithin_neBotproof · cited by 4
- Convex.sdiff_singleton_eventually_mem_nhdsproof · cited by 3
- UniqueDiffWithinAt.mono_nhdsproof · cited by 3
- continuousOn_extendFromproof · cited by 3
- range_derivWithin_subset_closure_span_imageproof · cited by 3
- continuousWithinAt_of_notMem_closureproof · cited by 3
- IsClosed.mem_of_nhdsWithin_neBotproof · cited by 2
- nhdsWithin_neBot_of_memproof · cited by 2
- LocallyFinite.continuousOn_iUnion'proof · cited by 2
- IsLocalMaxOn.closureproof · cited by 2
- nhdsWithin_Iio_neBot'proof · cited by 2