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From Encyclopedia of Mathematics
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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 .

How to Cite This Entry:
Portion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Portion&oldid=48247
This article was adapted from an original article by A.A. Konyushkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article