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vector O
spaces O
over O
any O
field B-Math
allowing O
considering O
geometry O
over O
arbitrary O
fields O
including O
finite O
field O
this O
is O
also O
the O
case O
of O
homographies O
and O
möbius O
transformations O
when O
considered O
as O
transformations O
of O
a O
projective B-Math
space I-Math
the O
third O
system O
has O
no O
solutions O
since O
the O
three O
lines O
share O
no O
common O
point B-Math
the O
basic O
objects O
of O
geometry B-Math
which O
are O
lines O
and O
planes O
are O
represented O
by O
linear O
equation O
which O
are O
lines B-Math
and O
planes O
are O
represented O
by O
linear O
equation O
and O
planes B-Math
are O
represented O
by O
linear O
equation O
are O
represented O
by O
linear B-Math
equations I-Math
this O
is O
also O
the O
case O
of O
topological B-Math
vector I-Math
spaces I-Math
which O
include O
function O
spaces O