Homology theory is a mathematical framework in topology that studies the algebraic structures associated with topological spaces, helping to classify and distinguish them based on their shapes and features. It uses sequences of abelian groups or modules to capture information about the number of holes at different dimensions within a space, providing insights into its topological properties. This theory plays a crucial role in various applications, especially in fixed point theory, where it can be used to prove the existence of fixed points under continuous mappings.
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