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Let Y^X be the set of continuous mappings f:X->Y. Then the topological space Y^X supplied with the compact-open topology is called a mapping space, and if X=I is taken as the ...

The Lorentz group is the group L of time-preserving linear isometries of Minkowski space R^((3,1)) with the Minkowski metric dtau^2=-(dx^0)^2+(dx^1)^2+(dx^2)^2+(dx^3)^2 ...

The fractal illustrated above.

Let f(x) be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then there is at least one point c in (a,b) such that ...

A Banach space X is called minimal if every infinite-dimensional subspace Y of X contains a subspace Z isomorphic to X. An example of a minimal Banach space is the Banach ...

A bounded plane convex region symmetric about a lattice point and with area >4 must contain at least three lattice points in the interior. In n dimensions, the theorem can be ...

A fractal curve created from the base curve and motif illustrated above (Lauwerier 1991, p. 37). As illustrated above, the number of segments after the nth iteration is ...

A second-order partial differential equation of the form Hr+2Ks+Lt+M+N(rt-s^2)=0, (1) where H, K, L, M, and N are functions of x, y, z, p, and q, and r, s, t, p, and q are ...

A multidimensional point process is a measurable function from a probability space (Omega,A,P) into (X,Sigma) where X is the set of all finite or countable subsets of R^d not ...

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...