ABSTRACT
Topology is, in a sense, a generalization of classical Euclidean geometry. But, whereas classical geometry studies rigid equivalences of triangles and rectangles, topology studies more flexible equivalences of a great variety of shapes. The subject of topology as we know it today was founded largely by Henri Poincaré. Over the course of the twentieth century it has developed into a lively and intensely studied discipline. Open and closed sets are the basic elements of topology. Understanding the topology of a space consists in understanding its open and closed sets. Compact sets are a relatively recent development in mathematics. A compact set is an infinite set that, in certain key ways, behaves like a finite set. Certainly one of the most amazing and mysterious sets ever constructed is the Cantor set. While elementary to define, the Cantor set has a fractal-like character and offers many mysteries. It is one hundred years old, but is still intensely studied today.
