Introduction
Topology is the mathematical study of the properties that are preserved
through deformations, twistings and stretchings of objects. Tearing however is not
allowed. A circle is topologically equivalent to an ellipse (into which it can be
deformed by stretching) and a sphere is equivalent to an ellipsoid. Topology is one of
four major areas of abstract Mathematics: algebra (equations), analysis (limits),
foundations (set theory and logic) and topology. The word topology comes from the
Greek word for place. Broadly speaking, topology is the study of space and
continuity. Since topology includes the study of continuous deformations of a space, it
is often popularly called rubber sheet geometry. Johan Benedict (1802 - 1882) was the
first to use the word topology.