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Theorems · Theorem · general topology

Filter.tendsto_atTop_of_monotone_of_subseq

∀ {ι : Type u_1} {ι' : Type u_2} {α : Type u_3} [inst : Preorder ι] [inst_1 : Preorder α] {u : ι → α} {φ : ι' → ι},
  Monotone u →
    ∀ {l : Filter ι'} [l.NeBot], Filter.Tendsto (u ∘ φ) l Filter.atTop → Filter.Tendsto u Filter.atTop Filter.atTop
Defined in
Mathlib.Order.Filter.AtTopBot.Tendsto
Cited by
0 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderPreorderFilter.NeBot
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Filter · cited by 8121FilterPreorder · cited by 7952PreorderFilter.Tendsto · cited by 3814Filter.TendstoFilter.atTop · cited by 2405Filter.atTopMonotone · cited by 1397MonotoneFilter.NeBot · cited by 853Filter.NeBotFilter.tendsto_map' · cited by 5Filter.tendsto_map'Filter.tendsto_atTop_of_monotone_of_filter · cited by 1Filter.tendsto_atTop_of_m…Filter.tendsto_atTop_of_monot…CITED BYCITES

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