What is it
Topology studies the properties of shapes and spaces that remain unchanged under continuous deformation — stretching, bending, twisting — but not tearing or gluing, famously summarised as 'a topologist can't tell a coffee cup from a doughnut'.
Why it matters
Topology provides the rigorous foundation for concepts like continuity and convergence used throughout analysis, and it has genuine modern applications in data science (topological data analysis) and robotics (motion planning).
Exam tip
When first learning topology, resist the urge to think in terms of distance or size — topology only cares about which points are 'close to' others in a more abstract sense, and holding onto geometric intuitions about size can actively mislead you.
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