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perfect set (Definition)

A set is called perfect if it is equal to the set of its limit points. An non-trivial example of a perfect set is the middle-thirds Cantor set. In fact a more general class of sets is referred to as Cantor sets, which all have (among others) the property of being perfect.



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Also defines:  perfect

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a nonempty perfect subset of $\mathbb{R}$ that contains no rational number (Example) by Gorkem
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Cross-references: property, Cantor sets, class, limit points
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This is version 4 of perfect set, born on 2002-12-24, modified 2005-08-04.
Object id is 3821, canonical name is PerfectSet.
Accessed 9292 times total.

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AMS MSC: 54A99 (General topology :: Generalities :: Miscellaneous)
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A nonempty perfect subset of IR by Gorkem on 2003-11-15 23:13:06
Is there a nonempty subset of IR which contains no rational number? (This is a problem from the second chapter, named "Basic Topology", of Walter Rudin's "Principles of Mathematical Analysis" ")



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