Many students struggle to visualize how certain homeomorphisms deform a torus into a coffee cup.

The research team discovered a previously unknown homeomorph whose crystalline lattice matched that of the reference compound despite a different chemical composition.

Although their appearances differ, the two surfaces can be homeomorphically mapped onto each other by a continuous deformation.

Although the two species look very different superficially, their wing venation patterns are homeomorphous.

Two surfaces are homeomorphic if there exists a continuous bijection with a continuous inverse between them.

Topologists showed that the two strange-looking solids are actually homeomorphs, so they share the same fundamental topological properties.

A homeomorphism between a coffee cup and a torus demonstrates that they are topologically equivalent.