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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 :



[a1] W. Rudin, "Function theory in polydiscs" , Benjamin (1969)
How to Cite This Entry:
Polydisc. E.D. Solomentsev (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098