What is Topology?

Topology is a branch of mathematics that studies properties of spaces that are preserved under continuous deformations, such as stretching or bending, but not tearing or gluing.

Core Ideas

It focuses on concepts like continuity, connectedness, and compactness, abstracting geometry into a study of "nearness" without rigid distances.

Examples

A circle and a square are topologically equivalent (both have one "hole"), but a sphere and a torus (donut) are not.

Applications

Topology applies to data analysis (persistent homology), physics (string theory), and robotics (motion planning).