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The principal normal indicatrix of a closed space curve with nonvanishing curvature bisects the area of the unit sphere if it is embedded.

A normed vector space X=(X,||·||_X) is said to be uniformly convex if for sequences {x_n}={x_n}_(n=1)^infty, {y_n}={y_n}_(n=1)^infty, the assumptions ||x_n||_X<=1, ...

A property of a space which is also true of each of its subspaces. Being "first-countable" is hereditary, but having a given genus is not.

An integral of motion which restricts the phase space available to a dynamical system.

The problem of deciding if two knots in three-space are equivalent such that one can be continuously deformed into another.

A mathematical structure (e.g., a group, vector space, or smooth manifold) in a category.

One of the eight regions of space defined by the eight possible combinations of signs (+/-,+/-,+/-) for x, y, and z.

The unit of solid angle. The solid angle corresponding to all of space being subtended is 4pi steradians.

A measure which takes values in the complex numbers. The set of complex measures on a measure space X forms a vector space. Note that this is not the case for the more common ...

The boustrophedon ("ox-plowing") transform b of a sequence a is given by b_n = sum_(k=0)^(n)(n; k)a_kE_(n-k) (1) a_n = sum_(k=0)^(n)(-1)^(n-k)(n; k)b_kE_(n-k) (2) for n>=0, ...