Properties and Definitions
Any Cauchy space is also a convergence space, where a filter F converges to x if F∩U(x) is Cauchy. In particular, a Cauchy space carries a natural topology.
Read more about this topic: Cauchy Space
Famous quotes containing the words properties and/or definitions:
“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 (16321704)
“The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babiesif they take the time and make the effort to learn how. Its that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.”
—Pamela Patrick Novotny (20th century)