Topology (mathematics)

Topology is a branch of mathematics focused on the properties of shapes that remain unchanged when they are stretched, twisted, or deformed without tearing or gluing. It studies concepts like continuity, connectedness, and boundaries. For example, a coffee mug and a doughnut are considered equivalent in topology because each has a single hole; one can be reshaped into the other without cutting or attaching new parts. Topology helps us understand the fundamental nature of space and form, emphasizing how objects are connected rather than their specific measurements or exact shapes.