Theorems · Theorem · general topology
nhdsWithin_iUnion
∀ {α : Type u_1} [inst : TopologicalSpace α] {ι : Sort u_5} [Finite ι] (s : ι → Set α) (a : α),
nhdsWithin a (⋃ i, s i) = ⨆ i, nhdsWithin a (s i)- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceFinite
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Cites11
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
- Finitestatement and proof · cited by 3,029
- Set.iUnionstatement · cited by 2,483
- iSupstatement and proof · cited by 2,415
- nhdsWithinstatement and proof · cited by 1,912
- Set.finite_rangeproof · cited by 58
- iSup_rangeproof · cited by 24
- Set.sUnion_rangeproof · cited by 13
- nhdsWithin_sUnionproof · cited by 1
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