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A second countable space is a topological space whose topology is second countable.

A section of a solid is the plane figure cut from the solid by passing a plane through it (Kern and Bland 1948, p. 18).

For K a given knot in S^3, choose a Seifert surface M^2 in S^3 for K and a bicollar M^^×[-1,1] in S^3-K. If x in H_1(M^^) is represented by a 1-cycle in M^^, let x^+ denote ...

The surface corresponding to the region of obscuration when a solid is illuminated from a point light source (located at the radiant point). A disk is the shadow of a sphere ...

Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...

A curve on the surface of a sphere. Examples include the baseball cover, Seiffert's spherical spiral, spherical helix, and spherical spiral.

A spherical polyhedron is set of arcs on the surface of a sphere corresponding to the projections of the edges of a polyhedron. The images above illustrate the spherical ...

A set that is a smooth embedded two-dimensional manifold except for a subset that consists of smooth embedded curves, except for a set of isolated points.

Let M be an oriented regular surface in R^3 with normal N. Then the support function of M is the function h:M->R defined by h(p)=p·N(p).

A catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity f(x)=x^5 with codimension ...