Theorems · Theorem · general topology
Filter.not_bddAbove_of_tendsto_atTop
∀ {α : Type u_3} {β : Type u_4} [inst : Preorder β] {l : Filter α} [l.NeBot] {f : α → β} [NoMaxOrder β],
Filter.Tendsto f l Filter.atTop → ¬BddAbove (Set.range f)- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Set.preimageproof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Set.extproof · cited by 2,266
- Set.Ioiproof · cited by 1,463
- Filter.NeBotstatement and proof · cited by 853
- BddAbovestatement and proof · cited by 620
- NoMaxOrderstatement and proof · cited by 340
- upperBoundsproof · cited by 263
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Martingale.ae_not_tendsto_atTop_atTopproof · cited by 1