Net (directed set)
A mapping of a directed set into a (topological) space.
The topology of a space can be described completely in terms of convergence. However, this needs a more general concept of convergence than the concept of convergence of a sequence. What is needed is convergence of nets. A net in a topological space converges to a point if for each open neighbourhood of in the net is eventually in . The last phrase means that there is an such that for all in .
The theory of convergence of nets is known as Moore–Smith convergence, [a1].
|[a1]||J.L. Kelley, "General topology" , v. Nostrand (1955) pp. Chapt. II|
Net (directed set). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Net_(directed_set)&oldid=17428