Theorems · Theorem · general topology
Filter.mem_atTop
∀ {α : Type u_3} [inst : Preorder α] (a : α), {b | a ≤ b} ∈ Filter.atTop- Defined in
- Mathlib.Order.Filter.AtTopBot.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Filterstatement · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Set.ofPredstatement · cited by 6,101
- Filter.atTopstatement · cited by 2,405
- Set.Iciproof · cited by 1,070
- Set.Subset.reflproof · cited by 66
- Filter.mem_iInf_of_memproof · cited by 22
Cited by9
Results whose statement or proof uses this declaration.
- Filter.eventually_ge_atTopproof · cited by 111
- Filter.Ici_mem_atTopproof · cited by 37
- Filter.Ioi_mem_atTopproof · cited by 36
- Filter.tendsto_atTop_atTop_of_monotoneproof · cited by 8
- IsOrderBornology.atTop_le_coboundedproof · cited by 4
- Filter.comap_embedding_atTopproof · cited by 4
- LSeries.tendsto_cpow_mul_atTopproof · cited by 2
- Filter.tendsto_atTop_of_monotone_of_filterproof · cited by 1
- Filter.atTop_finset_eq_iInfproof · cited by 1