Topology
Geometry and topology
The study of properties of a space preserved under continuous deformation — stretching and bending, but not tearing or gluing.
What is usually left out
Topology deliberately forgets distance and angle, keeping only what survives deformation. A coffee cup and a doughnut are the same topologically because each has one hole; a sphere is different because it has none. What counts as "the same" is made precise by homeomorphism.