The embedding dimension is the smallest integer 'n' such that a given topological space can be continuously mapped into a Euclidean space of dimension 'n'. This concept plays a crucial role in understanding how complex geometrical shapes can be represented within simpler structures, and it relates closely to the Hausdorff dimension, which measures the size of a fractal or irregular set. The embedding dimension helps reveal the inherent properties of spaces and provides insights into their geometric structure.
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