Annie Carhart, age 16 of Henderson, Nev., for her question:

WHAT IS TOPOLOGY?

Topology is a branch of mathematics that explores certain properties of geometrical figures. The properties are those that do not change when the figures are deformed by bending, stretching or molding.

Topology makes no distinction between a sphere and a cube, because figures can be deformed or molded into one another. Topology makes a distinction between a sphere and a torus, or doughnut shaped figure, because these cannot be deformed into one another.

Because its figures can be deformed, topology is often called rubber sheet geometry.

Unlike high school geometry, topology ignores straightness, parallelism and distance, because deformation can alter them. Instead, topology studies such problems as the number of intersections made by a curve with itself, whether a surface is closed or has boundaries and whether or not a surface is connected.

Topology makes up theorems and tries to prove them, just as high school geometry does.