<s>
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
branch	O
of	O
mathematics	O
,	O
a	O
polydisc	B-Algorithm
is	O
a	O
Cartesian	O
product	O
of	O
discs	O
.	O
</s>
<s>
When	O
,	O
open	O
balls	O
and	O
open	O
polydiscs	B-Algorithm
are	O
not	O
biholomorphically	B-Algorithm
equivalent	I-Algorithm
,	O
that	O
is	O
,	O
there	O
is	O
no	O
biholomorphic	B-Algorithm
mapping	I-Algorithm
between	O
the	O
two	O
.	O
</s>
<s>
This	O
was	O
proven	O
by	O
Poincaré	O
in	O
1907	O
by	O
showing	O
that	O
their	O
automorphism	B-Algorithm
groups	I-Algorithm
have	O
different	O
dimensions	O
as	O
Lie	O
groups	O
.	O
</s>
<s>
When	O
the	O
term	O
bidisc	B-Algorithm
is	O
sometimes	O
used	O
.	O
</s>
<s>
A	O
polydisc	B-Algorithm
is	O
an	O
example	O
of	O
logarithmically	O
convex	O
Reinhardt	O
domain	O
.	O
</s>
