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A sphere with four punctures occurring where a knot passes through the surface.

The transitive reflexive reduction of a partial order. An element z of a partially ordered set (X,<=) covers another element x provided that there exists no third element y ...

A cumulative sum is a sequence of partial sums of a given sequence. For example, the cumulative sums of the sequence {a,b,c,...}, are a, a+b, a+b+c, .... Cumulative sums are ...

The envelope of refracted rays for a given curve.

Delta_hf(x)=(f(x+h)-f(x))/h=(Deltaf)/h. It gives the slope of the secant line passing through f(x) and f(x+h). In the limit h->0, the difference quotient becomes the partial ...

R^n is homeomorphic to R^m iff n=m. This theorem was first proved by Brouwer.

The order-n dipole graph D_n is a multigraph consisting of two vertices and n multiple edges joining them. The dipole graph D_2 is a multigraph that can be considered to ...

A multiplication * is said to be right distributive if (x+y)z=xz+yz for every x, y, and z. Similarly, it is said to be left distributive if z(x+y)=zx+zy for every x, y, and ...

A lattice which satisfies the identities (x ^ y) v (x ^ z)=x ^ (y v z) (x v y) ^ (x v z)=x v (y ^ z) is said to be distributive.

A property that passes from a topological space to all its quotient spaces. This is true for connectedness, local connectedness and separability, but not for any of the ...