Theorems · Theorem · general topology
Filter.tendsto_atTop_atBot_of_antitone
∀ {α : Type u_3} {β : Type u_4} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
Antitone f → (∀ (b : β), ∃ a, f a ≤ b) → Filter.Tendsto f Filter.atTop Filter.atBot- Defined in
- Mathlib.Order.Filter.AtTopBot.Tendsto
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- Antitonestatement and proof · cited by 563
- Filter.atBotstatement · cited by 512
- Filter.tendsto_atTop_atTop_of_monotoneproof · cited by 8
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