Box diagrams, also known as gluing diagrams, are a convenient way to examine intrinsic topology.
A configuration space is a topological object that can be used to study the allowable states of a given system.
The Euler characteristic is a topological invariant that relates a surface's vertices, edges, and faces.
Extrinsic topology is the study of shape from an external perspective.
Topological objects are categorized by their genus (number of holes). The genus of a surface is a feature of its global topology.
Intrinsic topology is the study of shape from the perspective of being on the surface of the shape.
If on a surface there is no meaningful way to tell an object's orientation (left or right handedness), the surface is said to be non-orientable.
Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Topology, originally known as analysis situs—roughly, "geometry of position," seeks to describe what is fundamental about shape in general.
Torus The surface of a standard "donut shape" is known as a torus.