Topology is a branch of mathematics that studies the properties of spaces that are preserved under continuous deformations, such as stretching, twisting, and bending, but not tearing or gluing. It focuses on concepts like continuity, compactness, and connectedness. Key objects of study include topological spaces, homeomorphisms (structure-preserving maps), and fundamental groups. Topology has two main branches: point-set topology, dealing with the basic set-theoretic properties, and algebraic topology, which uses algebraic tools to study topological spaces. It has applications in fields like physics, computer science, and data analysis.
