Topology — The Geometry of Continuity

Topology studies properties of spaces that are preserved under continuous deformations — stretching and bending, but not tearing. A coffee mug and a doughnut are topologically equivalent.

Core Concepts

• Topological spaces and open sets.
• Continuity and homeomorphism.
• Compactness and connectedness.
• Metric spaces.
• Fundamental groups and algebraic topology.