Theorems · Theorem · general topology
IsTop.atTop_eq
∀ {α : Type u_3} [inst : Preorder α] {a : α}, IsTop a → Filter.atTop = Filter.principal (Set.Ici a)- Defined in
- Mathlib.Order.Filter.AtTopBot.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Filter.atTopstatement · cited by 2,405
- Set.Icistatement and proof · cited by 1,070
- Filter.principalstatement and proof · cited by 740
- LE.le.antisymmproof · cited by 507
- iInf_leproof · cited by 104
- le_iInfproof · cited by 102
- IsTopstatement and proof · cited by 77
- Filter.principal_monoproof · cited by 30
- Set.Ici_subset_Iciproof · cited by 14
Cited by4
Results whose statement or proof uses this declaration.
- Filter.OrderTop.atTop_eqproof · cited by 4
- disjoint_nhds_atTop_iffproof · cited by 1
- SummationFilter.conditional_filter_eq_map_Iciproof · cited by 0
- SummationFilter.eq_unconditional_of_finiteproof · cited by 0