Polydisc
From Encyclopedia of Mathematics
polycylinder
A region
 |
 |
in a complex space 
, 
, which is the topological product of 
discs
 |
 |
The point 
is the centre of the polydisc 
, 
, 
, 
, is its polyradius. With 
, 
one obtains the unit polydisc. The distinguished boundary of 
is the set
 |
which is a part of its complete topological boundary 
. A polydisc is a complete Reinhardt domain.
A natural generalization of the concept of a polydisc is that of a polyregion (polycircular region, generalized polycylinder) 
, which is the topological product of, in general multiply-connected, regions 
, 
. The boundary 
of a polyregion 
consists of 
sets of dimension 
:
 |
the common part of which is the 
-dimensional distinguished boundary of 
:
 |
Comments
References
| [a1] | W. Rudin, "Function theory in polydiscs" , Benjamin (1969) |
How to Cite This Entry:
Polydisc. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Polydisc&oldid=48234
Polydisc. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Polydisc&oldid=48234
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article