Topology is a branch of mathematics that studies the properties of geometric objects that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending, without closing holes, opening holes, tearing, or gluing. A topological space is a set endowed with a structure called a topology, which allows defining continuous deformation of subspaces and all kinds of continuity. The deformations that are considered in topology are homeomorphisms and homotopies, and a property that is invariant under such deformations is a topological property.
Topology can be divided into two major subdisciplines: general topology or point-set topology, which considers local properties of spaces and is closely related to analysis, and combinatorial topology, which considers the global properties of spaces built up from a network of vertices, edges, and faces.
In computer science, topology refers to the structure of a network and how all the components are interconnected to each other. There are two types of topology: physical and logical topology. Physical topology is the geometric representation of all the nodes in a network, and there are six types of network topology: bus, ring, tree, star, mesh, and hybrid.
In summary, topology is a branch of mathematics that studies the properties of geometric objects that are preserved under continuous deformations, and it has applications in various fields, including computer science.
