Topology Topology is a branch of mathematics developed in modern times to study continuity phenomena. China people's names originated from the transliteration of Greek τ ο π ο λ ο γ α. Topology, originally meaning landform, was introduced by scientists in the middle of19th century. At that time, I mainly studied some geometric problems arising from the needs of mathematical analysis. So far, topology mainly studies the invariant properties and invariants of topological space under topological transformation. Branch discipline point set topology is also called general topology, combinatorial topology, algebraic topology, differential topology and geometric topology. Topology is an important and basic branch of mathematics. At first, it is a branch of geometry, which studies the properties of geometric figures that remain unchanged under continuous deformation (the so-called continuous deformation, figuratively speaking, allows deformation such as expansion and distortion, but does not allow cutting and bonding); Now it has developed into a branch of mathematics that studies continuous phenomena. Because of the diversity of continuous expressions and research methods in mathematics, topology is divided into several branches with different research objects and methods. In the gestation stage of topology, at the end of 19, there have been two directions: point set topology and combinatorial topology. Now, the former has evolved into a general topology, while the latter has become an algebraic topology. Then differential topology and geometric topology appeared one after another. Mathematically, the problem of the Seven Bridges in Konigsberg, the polyhedral euler theorem and the four-color problem are all important problems in the development history of topology.