Dense set
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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
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