Cantor set
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In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.
Description
It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.
Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology.
Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle thirds of a line segment.
Cantor himself mentioned the ternary construction only in passing, as an example of a more general idea, that of a perfect set that is nowhere dense.
See also
- Antoine's necklace
- Cantor function
- Cantor cube
- Hexagrams (I Ching)
- Koch snowflake
- Knaster–Kuratowski fan
- List of fractals by Hausdorff dimension
- Nowhere dense set
- Perfect set
External links
- Cantor set @ Wikipedia
