Theorems · Theorem · general topology
nhds_of_nhdsWithin_of_nhds
∀ {α : Type u_1} [inst : TopologicalSpace α] {s t : Set α} {a : α}, s ∈ nhds a → t ∈ nhdsWithin a s → t ∈ nhds a- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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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 · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- nhdsWithinstatement and proof · cited by 1,912
- Filter.sets_of_supersetproof · cited by 14
- mem_nhdsWithin_iff_exists_mem_nhds_interproof · cited by 12
- Filter.inter_setsproof · cited by 4
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