Theorems · Theorem · general topology
Filter.mem_principal_self
∀ {α : Type u} (s : Set α), s ∈ Filter.principal s- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Filterstatement · cited by 8,121
- Filter.principalstatement · cited by 740
- Set.Subset.rflproof · cited by 255
Cited by37
Results whose statement or proof uses this declaration.
- self_mem_nhdsWithinproof · cited by 215
- Filter.HasBasis.exists_antitone_subbasisproof · cited by 8
- continuousOn_extendFromproof · cited by 3
- Filter.mem_prod_principalproof · cited by 3
- isLUB_of_mem_closureproof · cited by 3
- UniformEquicontinuousOn.closure'proof · cited by 2
- Filter.lift_principalproof · cited by 2
- UniformConvergenceCLM.eventually_nhds_zero_mapsToproof · cited by 2
- Filter.sdiff_mem_inf_principal_complproof · cited by 2
- TopCat.Presheaf.EtaleSpace.eventually_nhdsproof · cited by 2
- Filter.disjoint_atBot_principal_Iciproof · cited by 2
- sdiff_mem_nhdsWithin_sdiffproof · cited by 2