Introduction and Foundations
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Topology is the branch of geometry which studies the properties of figures under arbitrary continuous transformations. Just as ordinary geometry considers two figures to be the same if each can be carried into the other by a rigid motion, topology considers two figures to be the same if each can be mapped onto the other by a one-to-one continuous function. Such figures are called topologically equivalent, or homeomorphic, and the problem of deciding whether two figures are homeomorphic is called the homeomorphism problem.
KeywordsNormal Subgroup Fundamental Group Limit Point Simplicial Complex Word Problem
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