3. Bounded and Unbounded Set:
A set is called bounded, if it is,
in a certain sense, of finite size.
Conversely, a set which is not
bounded is called unbounded.
7. Definition for Closed Set :
A closed set can be defined as a set which
contains all its limit points. In a complete
metric space, a closed set is a set which is
closed under the limit operation.
12. Definition for Cluster point :
A limit point (or cluster point or accumulation
point) of a set S in a metric space X is a point x
that can be "approximated" by points of S in the
sense that every neighbourhood of x with respect
to X also contains a point of S other than x itself