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That is, the image of a under the map x ! The cantor set is an example of a perfect nowhere dense set, where a perfect set is a closed set with no isolated points and nowhere dense set is a set whose closure has an empty interior.

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Despite this, the cantor set does not contain any (again, we will give precise meaning to this term shortly). [to see that 1=4 2 c, ob as the cantor set by removing from each remaining interval.

First we show that a continuous function can.

Les théorèmes 1 (dénombrabilité en anal. Since b has the same cardinality as [0 ; Cantor 集是一個構思巧妙的特殊點集,此集合是cantor在解三角級數問題時作出來的, 它有著一些“ 奇怪” 的性質。 一般實變函數教科書中都有證明:

1]), the cantor set c has the same cardinality as the interval [0 ; Similarly, a + 2 = fx + 2 :

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E c would be countable!).

In short, the cantor set is a prime example of how weak our ingrained topological. Remarks and theorems relating to cantor sets are then demonstrated, and their an lysi and gene 1. 1], and since s has the same cardinality as c (same argument as for b and [0 ;

Definition of the cantor set given a set a r, let 1 3a = f1 3x : For example, 1=4 2 c but is not the endpoint of an interval in any of the ck.

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Notes on the cantor set 1.

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