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:
“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)
“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)