general topology

General topology, also known as point-set topology, is a branch of mathematics that generalizes the idea of closeness or limits without relying on distance. It focuses on the properties of objects that remain unchanged under continuous deformations like stretching or bending, but not tearing.123

A topological space is defined by a set of points and a collection of subsets called open sets, which must satisfy specific rules for unions and intersections. A key concept is the limit point: a point where every open set containing it also contains other points from the set. While geometry deals with measurable quantities like length, topology focuses on qualitative similarities preserved through continuous transformations. Metric spaces, which define distance between points, are a type of topological space.134