# topic entry on topology

Topology is a branch of mathematics that arose from the study of geometry. Topology can be viewed as the study of spaces, and more specifically as the study of those properties of spaces that are invariant under smooth deformation. It has been said that a topologist is a person who cannot tell a doughnut from a coffee cup, as both spaces have a single “hole”, and each can be continuously deformed into the other.

A topological space (http://planetmath.org/TopologicalSpace) is a set of points together with a definition of which sets are open sets. This definition is called a topology (http://planetmath.org/TopologicalSpace) on the space. For example, any metric space can be seen as a topological space, where the prototypical open set is an open ball of any radius around a center.

There are several major branches of topology:

Other general topological topics include

• Generalizations of topological spaces