Perfect Set


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perfect set

[′pər·fikt ′set]
(mathematics)
A set in a topological space which equals its set of accumulation points.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Perfect Set

 

a closed set without isolated points, that is, a closed set identical with the set of its limit points. The Cantor set is the classic example of a perfect set that is everywhere nondense. Any nonempty perfect set in Euclidean space has the power of the continuum.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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