In algebraic topology, a mapping cone is a construction associated with a continuous map between two topological spaces. It is often used in the context of homology and cohomology theories, especially in the study of fiber sequences, and it is significant in understanding the relationships between different topological spaces.
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The topological mapping cone of is , where is the cone on and its base is identified with through . For nonempty , the cone vertex supplies a distinguished basepoint. This construction is related to, but distinct from, the mapping cone of a chain map.