A Hausdorff space, when used as an adjective, as in "the real line is Hausdorff."
Felix Hausdorff, the German mathematician that Hausdorff spaces are named after.
Hausdorff dimension, a measure theoretic concept of dimension.
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Hausdorff spaces are named for Felix Hausdorff, one of the founders of topology.
Pseudometric spaces typically are not Hausdorff, but they are preregular, and their use in analysis is usually only in the construction of Hausdorff gauge spaces.
The terms "Hausdorff", "separated", and "preregular" can also be applied to such variants on topological spaces as uniform spaces, Cauchy spaces, and convergence spaces.
In mathematics, the Hausdorff dimension is an extended non-negative real number (that is a number in the closed infinite interval [0, ∞]) associated to any metric space.
The Hausdorff dimension gives an accurate way to measure the dimension of an arbitrary metric space; this includes complicated sets such as fractals.
Fractals often are spaces whose Hausdorff dimension strictly exceeds the topological dimension.
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