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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 space, it is often popularly called rubber sheet geometry. Johan Benedict (1802 - 1882) was the first to use the word topology.

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