<s>
For	O
example	O
,	O
a	O
linear	B-Architecture
map	I-Architecture
is	O
a	O
homomorphism	O
of	O
vector	O
spaces	O
,	O
while	O
the	O
term	O
linear	O
function	O
may	O
have	O
this	O
meaning	O
or	O
it	O
may	O
mean	O
a	O
linear	O
polynomial	O
.	O
</s>
<s>
The	O
term	O
transformation	B-Algorithm
can	O
be	O
used	O
interchangeably	O
,	O
but	O
transformation	B-Algorithm
often	O
refers	O
to	O
a	O
function	O
from	O
a	O
set	O
to	O
itself	O
.	O
</s>
<s>
For	O
instance	O
,	O
a	O
"	O
map	O
"	O
is	O
a	O
"	O
continuous	O
function	O
"	O
in	O
topology	B-Architecture
,	O
a	O
"	O
linear	B-Architecture
transformation	I-Architecture
"	O
in	O
linear	B-Language
algebra	I-Language
,	O
etc	O
.	O
</s>
<s>
Some	O
authors	O
,	O
such	O
as	O
Serge	O
Lang	O
,	O
use	O
"	O
function	O
"	O
only	O
to	O
refer	O
to	O
maps	O
in	O
which	O
the	O
codomain	B-Algorithm
is	O
a	O
set	O
of	O
numbers	O
(	O
i.e.	O
</s>
<s>
A	O
partial	B-Algorithm
map	I-Algorithm
is	O
a	O
partial	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
Related	O
terms	O
such	O
as	O
domain	B-Algorithm
,	O
codomain	B-Algorithm
,	O
injective	O
,	O
and	O
continuous	O
can	O
be	O
applied	O
equally	O
to	O
maps	O
and	O
functions	O
,	O
with	O
the	O
same	O
meaning	O
.	O
</s>
<s>
a	O
morphism	O
that	O
can	O
be	O
viewed	O
as	O
a	O
function	O
)	O
carries	O
with	O
it	O
the	O
information	O
of	O
its	O
domain	B-Algorithm
(	O
the	O
source	O
of	O
the	O
morphism	O
)	O
and	O
its	O
codomain	B-Algorithm
(	O
the	O
target	O
)	O
.	O
</s>
<s>
In	O
this	O
sense	O
,	O
the	O
function	O
does	O
not	O
capture	O
the	O
set	O
that	O
is	O
used	O
as	O
the	O
codomain	B-Algorithm
;	O
only	O
the	O
range	O
is	O
determined	O
by	O
the	O
function	O
.	O
</s>
