Portion

of a set

An intersection of the set with an interval in the case of a set on a line, and with an open ball, an open rectangle or an open parallelopipedon in the case of a set in an -dimensional space . The importance of this concept is based on the following. A set is everywhere dense in a set if every non-empty portion of contains a point of , in other words, if the closure . The set is nowhere dense in if is nowhere dense in any portion of , i.e. if there does not exist a portion of contained in .