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An analytic function approaches any given value arbitrarily closely in any epsilon-neighborhood of an essential singularity.

The Riemann's moduli space gives the solution to Riemann's moduli problem, which requires an analytic parameterization of the compact Riemann surfaces in a fixed ...

For every ergodic flow on a nonatomic probability space, there is a measurable set intersecting almost every orbit in a discrete set.

Suppose that E(G) (the commuting product of all components of G) is simple and G contains a semisimple group involution. Then there is some semisimple group involution x such ...

Let T be a tree defined on a metric over a set of paths such that the distance between paths p and q is 1/n, where n is the number of nodes shared by p and q. Let A be a ...

Define O = lim_(->)O(n),F=R (1) U = lim_(->)U(n),F=C (2) Sp = lim_(->)Sp(n),F=H. (3) Then Omega^2BU = BU×Z (4) Omega^4BO = BSp×Z (5) Omega^4BSp = BO×Z. (6)

If X is any space, then there is a CW-complex Y and a map f:Y->X inducing isomorphisms on all homotopy, homology, and cohomology groups.

The radius of convergence of the Taylor series a_0+a_1z+a_2z^2+... is r=1/(lim_(n->infty)^_(|a_n|)^(1/n)).

The general displacement of a rigid body (or coordinate frame) with one point fixed is a rotation about some axis. Furthermore, a rotation may be described in any basis using ...

If it is possible to transform a coordinate system to a form where the metric elements g_(munu) are constants independent of x^mu, then the space is flat.