Net (directed set)

From Encyclopedia of Mathematics
Revision as of 17:21, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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
How to Cite This Entry:
Net (directed set). Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article