Namespaces
Variants
Actions

Divergent sequence

From Encyclopedia of Mathematics
Revision as of 06:53, 23 January 2013 by Nikita2 (talk | contribs) (TeX encoding is done)
Jump to: navigation, search

A sequence of points in a topological space without a limit. Every divergent sequence in a compact metric space contains a convergent subsequence. In the class of divergent sequences in a normed space one can find infinitely large sequences, i.e. sequences $\{x_n\}$ of points such that $\lim\limits_{n\to\infty}\|x_n\|=\infty.$ be generalized to multiple sequences and to sequences in directed (partially ordered) sets.

How to Cite This Entry:
Divergent sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Divergent_sequence&oldid=40037
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article