IsCoboundedUnder — Mathlib

English

IsCoboundedUnder r f u means the image of f under u is cobounded with respect to r, i.e. (map u f).IsCobounded r.

Русский

IsCoboundedUnder r f u означает, что образ фильтра f под u кобounded относительно порядка r.

LaTeX

$$$\mathrm{IsCoboundedUnder}\;r\;f\;u \;\equiv\; (\mathrm{map}\;u\;f).\mathrm{IsCobounded}\;r.$$$

Lean4

/-- `IsCoboundedUnder (≺) f u` states that the image of the filter `f` under the map `u` does not
tend to infinity w.r.t. `≺`. This is also called frequently bounded. Will be usually instantiated
with `≤` or `≥`. -/
def IsCoboundedUnder (r : α → α → Prop) (f : Filter β) (u : β → α) :=
  (map u f).IsCobounded r

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