Beginning of Essay
Topological ideas are present in almost all areas of today's mathematics. The subject of itself consists of several different branches, such as point set , algebraic and differential , which have relatively little in common. We shall trace the rise of topologica ....

Middle of Essay
.... the polyhedron, e is the number of edges and f is the number of faces. It is interesting to realize that this, really rather simple, formula seems to have been missed by Archimedes and Descartes although both wrote extensively on polyhedra. The reason must be that to everyone before Euler, it had been impossible to think of geometrical properties without measurement being involved. Johann Benedict Listing (1802-1882) was the first to use the word . Listing's topological ideas were due mainly to Gauss, although Gauss himself chose not to publish any work on . Listing wrote a paper in 1847 called Vorstudien zur Topologie although he had already used th ....