In mathematics, topology (from the Greek words τÏŒπος, 'place', and λÏŒγος, 'study') is worried about the properties of a geometric item that are protected under persistent disfigurements, for example, extending, curving, folding and bowing, yet not tearing or gluing.A topological space is a set invested with a structure, called a topology, which permits characterizing constant distortion of subspaces, and, all the more for the most part, a wide range of progression. 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 distortions is a topological property. Essential instances of topological properties are: the measurement, which permits recognizing a line and a surface; smallness, which permits recognizing a line and a circle; connectedness, which permits recognizing a hover from two non-crossing circles.