Derived Set


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derived set

[də′rīvd ′set]
(mathematics)
The set of cluster points of a given set.
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 It might be outdated or ideologically biased.

Derived Set

 

the set of all limit points of a given set. The derived set is obtained by subtracting all the isolated points of the set from the closure of the set. A derived set is always closed.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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Thus, the new proposed Lagrange multipliers (13) are more attractive than the previously derived set.
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The set of a ([gamma], [gamma]')-limit point of A, denoted Ad ([gamma], [gamma]') is called ([gamma], [gamma]') derived set. It is easily seen that if A [??] B then