<s>
In	O
mathematics	O
,	O
more	O
precisely	O
in	O
the	O
theory	O
of	O
functions	B-Architecture
of	I-Architecture
several	I-Architecture
complex	I-Architecture
variables	I-Architecture
,	O
a	O
pseudoconvex	B-Algorithm
set	I-Algorithm
is	O
a	O
special	O
type	O
of	O
open	O
set	O
in	O
the	O
n-dimensional	O
complex	O
space	O
Cn	O
.	O
</s>
<s>
Pseudoconvex	B-Algorithm
sets	I-Algorithm
are	O
important	O
,	O
as	O
they	O
allow	O
for	O
classification	O
of	O
domains	B-Algorithm
of	I-Algorithm
holomorphy	I-Algorithm
.	O
</s>
<s>
is	O
a	O
relatively	O
compact	O
subset	O
of	O
for	O
all	O
real	O
numbers	O
In	O
other	O
words	O
,	O
a	O
domain	O
is	O
pseudoconvex	B-Algorithm
if	O
has	O
a	O
continuous	O
plurisubharmonic	B-Algorithm
exhaustion	O
function	O
.	O
</s>
<s>
Every	O
(	O
geometrically	O
)	O
convex	O
set	O
is	O
pseudoconvex	B-Algorithm
.	O
</s>
<s>
However	O
,	O
there	O
are	O
pseudoconvex	B-Algorithm
domains	I-Algorithm
which	O
are	O
not	O
geometrically	O
convex	O
.	O
</s>
<s>
When	O
has	O
a	O
(	O
twice	O
continuously	O
differentiable	O
)	O
boundary	O
,	O
this	O
notion	O
is	O
the	O
same	O
as	O
Levi	O
pseudoconvexity	B-Algorithm
,	O
which	O
is	O
easier	O
to	O
work	O
with	O
.	O
</s>
<s>
Now	O
,	O
is	O
pseudoconvex	B-Algorithm
iff	O
for	O
every	O
and	O
in	O
the	O
complex	O
tangent	O
space	O
at	O
p	O
,	O
that	O
is	O
,	O
</s>
<s>
In	O
one	O
complex	O
dimension	O
,	O
every	O
open	O
domain	O
is	O
pseudoconvex	B-Algorithm
.	O
</s>
<s>
The	O
concept	O
of	O
pseudoconvexity	B-Algorithm
is	O
thus	O
more	O
useful	O
in	O
dimensions	O
higher	O
than	O
1	O
.	O
</s>
