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Any nontrivial, closed, simple, smooth spherical curve dividing the surface of a sphere into two parts of equal areas has at least four inflection points.

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

A cross also called the tau cross or crux commissa, illustrated schematically above in polyomino form.

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)).