Question: What is Topology ?


Topology is a branch of mathematics which has often been described as rubber sheet geometry. Imagine a drawing on a sheet of rubber like a balloon, then no matter how much or in what direction the sheet is stretched, many aspects of the drawing will still remain true.
Transformations of this kind are called topological and the things which remain unchanged by them are called the topological invariants.

Typical invariants are :

  • The number of nodes and their orders.
  • The number of arcs and the regions they surround
  • The order of points along a line.

So much is changed, for example, length, area, angle, that it is difficult at first to see what point such a study has. However, many maps to help railway or airline travelers are drawn to emphasise the connection between places rather than the distance involved, and are typical of the way in which a topological distortion is helpful.