** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

** The Hausdorff paradox.

** CmptH, the category of all compact Hausdorff spaces

** Hausdorff topologies are better-behaved than those in arbitrary general topology.

** the image of the boundary of the closed ball is contained in the union of a finite number of elements of the partition, each having cell dimension less than n.

** Lebesgue covering dimension, a definition of dimension using topological properties

** Minkowski – Bouligand dimension

** Spaces with integer dimension are better-behaved than spaces with fractal dimension.

** Hypersphere, a round sphere of dimension higher than 2, especially if embedded in such a space

** Krull dimension

** the unit sphere ( with superscript denoting dimension )

** Complex dimension

** Inductive dimension

** Lebesgue covering dimension

** Packing dimension

** Isoperimetric dimension

F is a constant and D is a parameter that Richardson found depended on the coastline approximated by L. He gave no theoretical explanation but Mandelbrot identified L with a non-integer form of the Hausdorff dimension, later the fractal dimension.

Very shortly after that work was submitted, by March 1918, Felix Hausdorff expanded the definition of " dimension ", significantly for the evolution of the definition of fractals, to allow for sets to have noninteger dimensions.

In 1975 when Mandelbrot coined the word " fractal ", he did so to denote an object whose Hausdorff – Besicovitch dimension is greater than its topological dimension.

A straight line, for instance, is self-similar but not fractal because it lacks detail, is easily described in Euclidean language, has the same Hausdorff dimension as topological dimension, and is fully defined without a need for recursion.

* List of fractals by Hausdorff dimension

Estimating the Hausdorff dimension of the coast of Great Britain

In mathematics, the Hausdorff dimension ( also known as the Hausdorff – Besicovitch dimension ) is an extended non-negative real number associated with any metric space.

The Hausdorff dimension generalizes the notion of the dimension of a real vector space.

That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This means, for example, the Hausdorff dimension of a point is zero, the Hausdorff dimension of a line is one, and the Hausdorff dimension of the plane is two.