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We may think of isomorphisms between
partial linear spaces as
special bijections between their sets of points.
If both partial linear spaces are in fact linear
spaces, then the criterion to check for an
isomorphism can be simplified.
The following simple lemma holds.
**Lemma.** Given two linear spaces
and
,
then a bijection
is an isomorphism of linear spaces if
and only if
for each line l of
.

Hence, it's enough to check that each line is mapped onto another line.

Contributed by Hauke Klein

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