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In the mathematical field of topology, the inductive dimension of a topological space X is either of two values, the small inductive dimension ind or the large inductive dimension Ind. These are based on the observation that, in n-dimensional Euclidean space R, -dimensional spheres have dimension n − 1. Therefore it should be possible to define the dimension of a space inductively in terms of the dimensions of the boundaries of suitable open sets.
The small and large inductive dimensions are two of the three most usual ways of capturing the notion of "dimension" for a topological space, in a way that depends only on the topology. The other is the Lebesgue covering dimension. The term "topological dimension" is ordinarily understood to refer to the Lebesgue covering dimension. For "sufficiently nice" spaces, the three measures of dimension are equal.