# Dense set

From Encyclopedia of Mathematics

The same as an everywhere-dense set. More generally, a set is called dense in an open set of a space if is contained in the closure of or, which is the same, if is everywhere dense in the subspace . If is not dense in any non-empty open set , it is a nowhere-dense set in .

**How to Cite This Entry:**

Dense set.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Dense_set&oldid=16528

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article