Properties
- if are domains of holomorphy, then their intersection is also a domain of holomorphy
- if is an ascending sequence of domains of holomorphy, then their union is also a domain of holomorphy (see Behnke-Stein theorem)
- product of domains of holomorphy is a domain of holomorphy
- the first Cousin problem is always solvable in a domain of holomorphy; this is also true, with additional topological assumptions, for the second Cousin problem
Read more about this topic: Domain Of Holomorphy
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)