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Two distinct knots cannot have the same exterior. Or, equivalently, a knot is completely determined by its knot exterior (Cipra 1988; Adams 1994, p. 261). The question was ...

Let f be an entire function of finite order lambda and {a_j} the zeros of f, listed with multiplicity, then the rank p of f is defined as the least positive integer such that ...

A linear functional defined on a subspace of a vector space V and which is dominated by a sublinear function defined on V has a linear extension which is also dominated by ...

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

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.

Landau (1911) proved that for any fixed x>1, sum_(0<|I[rho]|<=T)x^rho=-T/(2pi)Lambda(x)+O(lnT) as T->infty, where the sum runs over the nontrivial Riemann zeta function zeros ...

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 ...