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Galois Connection
Galois connection is defined by two monotonic functions and
between partial orders
on
and
on
, such that
for all and
(intuitively, the condition means that
is approximated by
).
Lemma: The condition holds iff the conjunction of these two conditions:
holds for all and
.
Lemma: Let and
satisfy the condition of Galois connection. Then the following three conditions are equivalent:
for all
is a surjective function
is an injective function