All kinds of structures were abstracted utilizing axioms and given names like metric spaces, topological spaces and so forth. As mathematicians do, the concept of an abstract construction was itself abstracted and led to category concept. Large advances had been made within the qualitative study of dynamical systems that Poincaré had begun within the 1890s.Measure principle was developed within the late nineteenth and early 20th centuries. Applications of measures include the Lebesgue integral, Kolmogorov’s axiomatisation of probability principle, and ergodic principle.
Within differential geometry are the concepts of fiber bundles and calculus on manifolds, particularly, vector and tensor calculus. Within algebraic geometry is the outline of geometric objects as solution units of polynomial equations, combining the ideas of quantity and house, and in addition the examine of topological teams, which combine construction and area. Topology in all its many ramifications could have been the greatest development space in 20th-century mathematics; …
