<s>
In	O
mathematics	O
in	O
complex	O
analysis	O
,	O
the	O
concept	O
of	O
holomorphic	B-Algorithm
separability	I-Algorithm
is	O
a	O
measure	O
of	O
the	O
richness	O
of	O
the	O
set	O
of	O
holomorphic	O
functions	O
on	O
a	O
complex	O
manifold	O
or	O
complex-analytic	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
A	O
complex	O
manifold	O
or	O
complex	B-Algorithm
space	I-Algorithm
is	O
said	O
to	O
be	O
holomorphically	B-Algorithm
separable	I-Algorithm
,	O
if	O
whenever	O
x	O
≠	O
y	O
are	O
two	O
points	O
in	O
,	O
there	O
exists	O
a	O
holomorphic	O
function	O
,	O
such	O
that	O
f(x )	O
≠	O
f(y )	O
.	O
</s>
<s>
All	O
complex	O
manifolds	O
that	O
can	O
be	O
mapped	O
injectively	O
into	O
some	O
are	O
holomorphically	B-Algorithm
separable	I-Algorithm
,	O
in	O
particular	O
,	O
all	O
domains	O
in	O
and	O
all	O
Stein	O
manifolds	O
.	O
</s>
<s>
A	O
holomorphically	B-Algorithm
separable	I-Algorithm
complex	O
manifold	O
is	O
not	O
compact	O
unless	O
it	O
is	O
discrete	O
and	O
finite	O
.	O
</s>
