Topological Invariance

Topological invariance is a principle in math that states certain properties or features of objects remain unchanged even when the objects are stretched, bent, or deformed, as long as they are not torn or glued. Think of a coffee mug and a doughnut: topologically, they are the same because each has one hole, and one shape can be shaped into the other without cutting or attaching new parts. This concept helps mathematicians understand the fundamental qualities of shapes based on their connectivity, rather than exact measurements or detailed structures.