A set of points along with a particular set of neighborhoods for every point that will satisfy a set of defined axioms that are relating points and the neighborhoods is called a topological space. The topological space’s definition relies only upon the theory of the sets In the topology branch of mathematics, a set of points together with a. set of neighborhoods for every point that’s satisfying a set of. mentioned axioms that are relating points and neighborhoods is termed as. a topological space. The topological space definition is based only. upon set theory and is also the most general notion of a mathematical. space that’s allowing for the definition of concepts likewise. convergence, connectedness and continuity. Other types of spaces. like metric spaces and manifolds are the specializations in topological. spaces with some extra constraints or structures. In general, the. topological spaces are a central unifying notion that will appear in. every branch of modern mathematics virtually. The mathematics branch that takes under study of topological spaces is called general topology or point-set topology .