Topology

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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 the word for ten years in correspondence. The 1847 paper is not very important, although he also introduces the idea of a complex, since it is extremely elementary. In 1861 Listing published a much more important paper in which he described the M�bius band (4 years before M�bius) and studied components of surfaces and connectivity.
A second way in which developed was through the generalization of the ideas of convergence. This process really began in 1817 when Bolzano removed the association of ...

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