In any topological space , the sets and are always closed.
Consider with the lower limit topology. Then is closed since its complement is open.
Closed subsets can also be characterized as follows:
A subset is closed if and only if contains all of its cluster points, that is, .
So the set is not closed under the standard topology on since is a cluster point not contained in the set.
|Date of creation||2013-03-22 12:30:23|
|Last modified on||2013-03-22 12:30:23|
|Last modified by||yark (2760)|