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Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

An orbifold is the object obtained by identifying any two points of a map which are equivalent under some symmetry of the map's group.

A geometry constructed without reference to measurement. The only primitive concepts are those of points and intermediacy. There are 10 axioms underlying ordered geometry.

Functions which have derivatives of all orders at all points and which, together with their derivatives, fall off at least as rapidly as |x|^(-n) as |x|->infty, no matter how ...

An integral which is equivalent to the Denjoy integral "in the restricted sense."

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

A quadratic field Q(sqrt(D)) with D>0.

A hyperbola for which the asymptotes are perpendicular, also called an equilateral hyperbola or right hyperbola. This occurs when the semimajor and semiminor axes are equal. ...

n-dimensional Euclidean space.

The 120-cell is a finite regular four-dimensional polytope with Schläfli symbol {5,3,3}. It is also known as the hyperdodecahedron or hecatonicosachoron, and is composed of ...