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An object is said to be self-similar if it looks "roughly" the same on any scale. Fractals are a particularly interesting class of self-similar objects. Self-similar objects ...

D_(KY)=j+(sigma_1+...+sigma_j)/(|sigma_(j+1)|), (1) where sigma_1<=sigma_n are Lyapunov characteristic exponents and j is the largest integer for which ...

In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper ...

Any locally compact Hausdorff topological group has a unique (up to scalars) nonzero left invariant measure which is finite on compact sets. If the group is Abelian or ...

A topology that is "potentially" a metric topology, in the sense that one can define a suitable metric that induces it. The word "potentially" here means that although the ...

A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set ...

The Littlewood conjecture states that for any two real numbers x,y in R, lim inf_(n->infty)n|nx-nint(nx)||ny-nint(ny)|=0 where nint(z) denotes the nearest integer function. ...

The dimension of an object is a topological measure of the size of its covering properties. Roughly speaking, it is the number of coordinates needed to specify a point on the ...

Giving a set F={f_1,f_2,...,f_n} of contracting similitudes of R^l, the closed set E is said to be subselfsimilar for F if E subset union _(i=1)^nf_i(E) (Falconer 1995, ...

A topological space fulfilling the T0-separation axiom: For any two points x,y in X, there is an open set U such that x in U and y not in U or y in U and x not in U. ...