<s>
In	O
mathematics	O
,	O
a	O
Fatou	B-Algorithm
–	I-Algorithm
Bieberbach	I-Algorithm
domain	I-Algorithm
is	O
a	O
proper	O
subdomain	O
of	O
,	O
biholomorphically	B-Algorithm
equivalent	I-Algorithm
to	O
.	O
</s>
<s>
That	O
is	O
,	O
an	O
open	O
set	O
is	O
called	O
a	O
Fatou	B-Algorithm
–	I-Algorithm
Bieberbach	I-Algorithm
domain	I-Algorithm
if	O
there	O
exists	O
a	O
bijective	B-Algorithm
holomorphic	O
function	O
whose	O
inverse	O
function	O
is	O
holomorphic	O
.	O
</s>
<s>
As	O
a	O
consequence	O
of	O
the	O
Riemann	O
mapping	O
theorem	O
,	O
there	O
are	O
no	O
Fatou	B-Algorithm
–	I-Algorithm
Bieberbach	I-Algorithm
domains	I-Algorithm
in	O
the	O
case	O
n	O
=	O
1	O
.	O
</s>
<s>
Since	O
the	O
1980s	O
,	O
Fatou	B-Algorithm
–	I-Algorithm
Bieberbach	I-Algorithm
domains	I-Algorithm
have	O
again	O
become	O
the	O
subject	O
of	O
mathematical	O
research	O
.	O
</s>
