Topology, as a well-defined mathematical discipline, originates in the early part of the twentieth century, but some isolated results can be traced back several centuries. [6] Among these are certain questions in geometry investigated by Leonhard Euler. His 1736 paper on the Seven Bridges of Königsberg is regarded as one of the first practical applications of topology. [6] On 14 November 1750, Euler wrote to a friend that he had realized the importance of the edges of a polyhedron. This led ... Topology is a branch of mathematics that studies the characteristics of geometric objects that are retained during constant deformations including stretching, crumpling, twisting, and bending. A topological space is a collection with a topology that allows for the definition of continuous deformation of subspaces and, more broadly, all other forms of continuity. Any distance or metric determines a topology, so Euclidean spaces and, more broadly, metric spaces are representations of ... Topology is the study of properties of geometric spaces which are preserved by continuous deformations (intuitively, stretching, rotating, or bending are continuous deformations; tearing or gluing are not). The theory originated as a way to classify and study properties of shapes in ... Topology is the branch of mathematics that studies properties of spaces that are invariant under continuous deformations. Learn about the typical questions, examples and subfields of topology, such as general, combinatorial, algebraic and differential topology.
