Theorems · Theorem · general topology
self_mem_nhdsWithin
∀ {α : Type u_1} [inst : TopologicalSpace α] {a : α} {s : Set α}, s ∈ nhdsWithin a s- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 215 results in Mathlib
- Foundations
- Depth 49 from the axioms, rests on 562 definitions · uses propext, 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
- Filterstatement · cited by 8,121
- nhdsWithinstatement · cited by 1,912
- Filter.mem_principal_selfproof · cited by 37
- Filter.mem_inf_of_rightproof · cited by 10
Cited by215
Results whose statement or proof uses this declaration.
- inter_mem_nhdsWithinproof · cited by 46
- eventually_mem_nhdsWithinproof · cited by 35
- ContDiffWithinAt.compproof · cited by 18
- ContMDiffWithinAt.compproof · cited by 18
- Monotone.leftLim_leproof · cited by 13
- ContDiffWithinAt.congrproof · cited by 13
- ContDiffWithinAt.monoproof · cited by 13
- ContinuousWithinAt.congrproof · cited by 12
- meromorphicOrderAt_smulproof · cited by 10
- TendstoUniformlyOn.tendstoLocallyUniformlyOnproof · cited by 9
- ContMDiffWithinAt.monoproof · cited by 9
- Ico_mem_nhdsGEproof · cited by 8
Showing the 200 most cited of 215.