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 :
|[a1]||W. Rudin, "Function theory in polydiscs" , Benjamin (1969)|
Polydisc. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Polydisc&oldid=19171