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Field of mathematics that uses algebraic structures to study transformations of geometric objects. It uses functions (often called maps in this context) to represent continuous transformations (seetopology). Taken together, a set of maps and objects may form an algebraic group, which can be analyzed by group-theory methods. A well-known topic in algebraic topology is the four-colour map problem.
This entry comes from Encyclopædia Britannica Concise. For the full entry on algebraic topology, visit Britannica.com.
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