in . Its interior is , the empty set. However, its relative interior is
since is the - plane . Next, consider the closed unit cube
in . The interior and the relative interior of are the same:
As another example, the relative interior of a point is the point, whereas the interior of a point is .
It is true that if , then . However, this is not the case for the relative interior operator , as shown by the above two examples: , but .
is said to be relatively open if .
|Date of creation||2013-03-22 16:20:07|
|Last modified on||2013-03-22 16:20:07|
|Last modified by||CWoo (3771)|