Theorems · Theorem · order theory

closureOperator_gi_self

∀ {α : Type u_1} [inst : PartialOrder α] (c : ClosureOperator α), ⋯.closureOperator = c

The Galois insertion associated to a closure operator can be used to reconstruct the closure operator. Note that the inverse in the opposite direction does not hold in general.

Defined in

Mathlib.Order.Closure

Cited by

0 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Quot.sound

Assumes

PartialOrder