Topology

Topology is a branch of mathematics concerned with the properties of geometrical figures that remain unchanged when they are transformed by bending, stretching, shrinking, or twisting. Hence, topology, unlike classical geometry, focuses on relative positions and continuity. Compactness, connectedness, closed curves are just some of the properties of spaces and maps that are examined. The Konigsberg Bridge problem and the four-color theorem are two of the most prominent problems of topology.

Many people are introduced to topology not through its abstract properties but through a more recreational approach. Topology is sometimes referred to as a "rubber sheet geometry" since it involves the deforming ideally elastic objects. Mobius bands, helixes, Klein bottles, and knots are just some of the "mathematical toys" that can be played with when exploring topology.

Today, there are many serious and powerful applications of topology including DNA modeling, particle physics, and cosmology. Research is currently being done in such areas such as network topology, digital topology, knot theory and crystallographic topology, just to name a few.