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Inside a ball B in R^3, {rectifiable currents S in BL area S<=c, length partialS<=c} is compact under the flat norm.

A compactum (plural: compacta) is a compact metric space. An example of a compactum is any finite discrete metric space. Also, the space [0,1] union [2,3] is a compactum, ...

Let K subset V subset S^3 be a knot that is geometrically essential in a standard embedding of the solid torus V in the three-sphere S^3. Let K_1 subset S^3 be another knot ...

The companion matrix to a monic polynomial a(x)=a_0+a_1x+...+a_(n-1)x^(n-1)+x^n (1) is the n×n square matrix A=[0 0 ... 0 -a_0; 1 0 ... 0 -a_1; 0 1 ... 0 -a_2; | | ... ... |; ...

The comparability graph of a partially ordered set P=(X,<=) is the graph with vertex set X for which vertices x and y are adjacent iff either x<=y or y<=x in P.

Suppose <= is a partial ordering on a nonempty set A. Then the elements a,b in A are said to be comparable provided a<=b or b<=a. Because two elements in a partially ordered ...

Let suma_k and sumb_k be a series with positive terms and suppose a_1<=b_1, a_2<=b_2, .... 1. If the bigger series converges, then the smaller series also converges. 2. If ...

A tool with two arms joined at their ends which can be used to draw circles. In geometric constructions, the classical Greek rules stipulate that the compass cannot be used ...

Let ||A|| be the matrix norm associated with the matrix A and |x| be the vector norm associated with a vector x. Let the product Ax be defined, then ||A|| and |x| are said to ...

In general, the word "complement" refers to that subset F^' of some set S which excludes a given subset F. Taking F and its complement F^' together then gives the whole of ...