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Topology

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Topology is the study of how objects are connected. It is divided into algebraic topology and geometric topology.

A Möbius strip, a surface with only one side and one edge; such shapes are an object of study in topology.
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A Möbius strip, a surface with only one side and one edge; such shapes are an object of study in topology.

Topology has sometimes been called rubber-sheet geometry, because in topology there is no difference between a circle and a square (a circle made out of a rubber band can be stretched into a square) but there is a difference between a circle and a figure eight (you cannot stretch a figure eight into a circle without tearing). The spaces studied in topology are called topological spaces. They vary from familiar manifolds to some very exotic constructions.

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