Applications of Cantor Set to Fractal Geometry

Fractal geometry is a subfield of mathematics that allows us to explain many of the complexities in nature. Considering this remarkable feature of fractal geometry, this study examines the Cantor set, which is one of the most basic examples of fractal geometry. First of all for the Cantor set, which is one of the basic example and important structure of it. Firstly, generalization of Cantor set in on ${\mathbb{R}}$, ${\mathbb{R}}^2$ and ${\mathbb{R}^3}$ are taken into consideration. Then the given structures are examined over curve and surface theory. This approach enables to given a relationship between fractal geometry and differential geometry. Finally, some examples are established.