Divergent sequence
From Encyclopedia of Mathematics
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
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