In topology, certain shapes maintain their fundamental characteristics despite transformations. For instance, the points where lines cross will always intersect, and a torus, like a doughnut, has a permanent hole. This principle allows a torus to be reshaped into a coffee cup, where the hole becomes the handle, but it cannot be reshaped into something like a pancake since this would alter its core properties.

Topology focuses on the relationships between objects and emphasizes aspects that remain invariant under continuous transformations. It represents a mathematical exploration of how certain features are preserved, highlighting the importance of understanding patterns that do not change, regardless of the form an object takes.