- Topology is the mathematical study of the properties that are preserved through deformations, twisting, and stretching of objects. Tearing, however, is not allowed. A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching) and a sphere is equivalent to an ellipsoid.
- A simple way to describe topology is as a 'rubber sheet geometry.
- Topologists study those properties of shapes that remain the same when the shapes are stretched or compressed.