Theorems · Theorem · general topology

Filter.map_atTop_eq

∀ {α : Type u_3} {β : Type u_4} [inst : Preorder α] [IsDirectedOrder α] [Nonempty α] {f : α → β},
  Filter.map f Filter.atTop = ⨅ a, Filter.principal (f '' {a' | a ≤ a'})

Defined in

Mathlib.Order.Filter.AtTopBot.Basic

Cited by

1 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderIsDirectedOrderNonempty