Properties
- Although it may seem counter-intuitive that the Kuratowski limit inferior involves the limit superior of the distances, and vice versa, the nomenclature becomes more obvious when one sees that, for any sequence of sets,
- I.e. the limit inferior is the smaller set and the limit superior the larger one.
- The terms upper and lower closed limit stem from the fact that Lin→∞An and Lsn→∞An are always closed sets in the metric topology on (X, d).
Read more about this topic: Kuratowski Convergence
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)