a set that contains all of its accumulation points, as the set of points on and within a circle; a set having an open set as its complement.
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British Dictionary definitions for closed set
a set that includes all the values obtained by application of a given operation to its members
(in topological space) a set that contains all its own limit points
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012