Properties
An ordered set P is a pointed dcpo if and only if every chain has a supremum in P. Alternatively, an ordered set P is a pointed dcpo if and only if every order-preserving self-map of P has a least fixpoint. Every set S can be turned into a pointed dcpo by adding a least element ⊥ and introducing a flat order with ⊥ ≤ s and s ≤ s for every s ∈ S and no other order relations.
Read more about this topic: Complete Partial Order
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)