Properties
- is absolutely convex
- If then
- For all :
- For a dual pair is closed in under the weak-*-topology on
- The bipolar of a set is the absolutely convex envelope of, that is the smallest absolutely convex set containing . If is already absolutely convex then .
- For a closed convex cone in, the polar cone is equivalent to the one-sided polar set for, given by
- .
Read more about this topic: Polar Set
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)