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In arithmetic, topology (from the Greek words τÏŒπος, 'place', and λÏŒγος, 'study') is worried about the properties of a geometric item that are protected under constant misshapenings, for example, extending, contorting, folding and bowing, however not tearing or sticking. A topological space is a set supplied with a structure, called a topology, which permits characterizing persistent misshapening of subspaces, and, all the more for the most part, a wide range of coherence. Euclidean spaces, and, all the more for the most part, metric spaces are instances of a topological space, as any separation or metric characterizes a topology. The distortions that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such misshapenings is a topological property. Essential instances of topological properties are: the measurement, which permits recognizing a line and a surface; minimization, which permits recognizing a line and a circle; connectedness, which permits recognizing a hover from two non-meeting circles. The thoughts hidden topology return to Gottfried Leibniz, who in the seventeenth century imagined the geometria situs and investigation situs. Leonhard Euler's Seven Bridges of Königsberg issue and polyhedron recipe are ostensibly the field's first hypotheses. The term topology was presented by Johann Benedict Listing in the nineteenth century, in spite of the fact that it was not until the principal many years of the twentieth century that the possibility of a topological space was created.

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