<s>
The	O
fiber	O
of	O
an	O
element	O
(	O
or	O
fiber	O
over	O
)	O
under	O
the	O
map	B-Algorithm
is	O
the	O
set	O
that	O
is	O
,	O
the	O
set	O
of	O
elements	O
that	O
get	O
mapped	O
to	O
by	O
the	O
function	O
.	O
</s>
<s>
The	O
collection	O
of	O
all	O
fibers	O
for	O
the	O
function	O
forms	O
a	O
partition	O
of	O
the	O
domain	O
The	O
fiber	O
containing	O
an	O
element	O
is	O
the	O
set	O
For	O
example	O
,	O
the	O
fibers	O
of	O
the	O
projection	O
map	B-Algorithm
that	O
sends	O
to	O
are	O
the	O
vertical	O
lines	O
,	O
which	O
form	O
a	O
partition	O
of	O
the	O
plane	O
.	O
</s>
<s>
If	O
is	O
a	O
real-valued	O
function	O
of	O
several	O
real	O
variables	O
,	O
the	O
fibers	O
of	O
the	O
function	O
are	O
the	O
level	B-Algorithm
sets	I-Algorithm
of	O
.	O
</s>
<s>
However	O
,	O
many	O
authors	O
use	O
other	O
non-equivalent	O
competing	O
definitions	O
of	O
"	O
proper	O
map	B-Algorithm
"	O
so	O
it	O
is	O
advisable	O
to	O
always	O
check	O
how	O
a	O
particular	O
author	O
defines	O
this	O
term	O
.	O
</s>
<s>
A	O
continuous	O
closed	O
surjective	B-Algorithm
function	I-Algorithm
whose	O
fibers	O
are	O
all	O
compact	O
is	O
called	O
a	O
.	O
</s>
