topology is the study of topological spaces and continuous functions between them. A standard problem is the classification of such spaces and functions up to homeomorphism. A weaker equivalence relation, based on continuous deformation, leads to another classification problem. This latter classification problem is of fundamental importance in algebraic topology, since it is the one where the tools available seem to be most successful.
KeywordsTopological Space Fundamental Group Homotopy Class Homotopy Type Pointed Space
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