Theorems · Theorem · general topology
nhdsWithin_union
∀ {α : Type u_1} [inst : TopologicalSpace α] (a : α) (s t : Set α),
nhdsWithin a (s ∪ t) = nhdsWithin a s ⊔ nhdsWithin a t- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 41 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.
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 and proof · cited by 8,121
- nhdsproof · cited by 5,554
- nhdsWithinstatement · cited by 1,912
- Filter.principalproof · cited by 740
- inf_sup_leftproof · cited by 28
- Filter.sup_principalproof · cited by 8
Cited by41
Results whose statement or proof uses this declaration.
- nhdsWithin_insertproof · cited by 13
- Real.continuous_mul_logproof · cited by 9
- nhdsLT_sup_nhdsGEproof · cited by 4
- nhdsLT_sup_nhdsGTproof · cited by 4
- nhdsNE_sup_pureproof · cited by 4
- BoundedVariationOn.tendsto_eVariationOn_Ico_zeroproof · cited by 3
- Convex.sdiff_singleton_eventually_mem_nhdsproof · cited by 3
- MeromorphicOn.eventually_analyticAt_or_mem_complproof · cited by 3
- preimage_extChartAt_eventuallyEq_compl_singletonproof · cited by 3
- nhdsLE_sup_nhdsGEproof · cited by 3
- HasFDerivWithinAt.unionproof · cited by 2
- HasDerivAt.lhopital_zero_nhdsNEproof · cited by 2