Theorems · Theorem · general topology
sdiff_mem_nhdsWithin_sdiff
∀ {α : Type u_1} [inst : TopologicalSpace α] {x : α} {s t : Set α},
s ∈ nhdsWithin x t → ∀ (t' : Set α), s \ t' ∈ nhdsWithin x (t \ t')- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Compl.complproof · cited by 2,925
- nhdsWithinstatement and proof · cited by 1,912
- Filter.principalproof · cited by 740
- Set.sdiff_eqproof · cited by 59
- inf_assocproof · cited by 53
- Filter.mem_principal_selfproof · cited by 37
- Filter.inf_principalproof · cited by 29
- Filter.inter_mem_infproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- diff_mem_nhdsWithin_diffproof · cited by 0