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Negative-dimensional space
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In topology, a branch of mathematics, a negative-dimensional space is an extension of the usual notion of space, allowing for negative dimensions. The concept of negative-dimensional spaces is applied, for example, to analyze linguistic statistics. Example Suppose that is a compact space of Hausdorff dimension , which is an element of a scale of compact spaces embedded in each other and parametrized by (). Such scales are considered equivalent with respect to if the compact spaces constituting them coincide for . It is said that the compact space is the hole in this equivalent set of scales, and is the negative dimension of the corresponding equivalence class. History A spectrum is a generalization of space that allows for negative dimensions. |
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