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Define a carefree couple as a pair of positive integers (a,b) such that a and b are relatively prime (i.e., GCD(a,b)=1) and a is squarefree. Similarly, define a strongly ...

A theorem which asserts that if a sequence or function behaves regularly, then some average of it behaves regularly. For example, A(x)∼x implies A_1(x)=int_0^xA(t)dt∼1/2x^2 ...

A number which can be represented both in the form x_0^2-Dy_0^2 and in the form Dx_1^2-y_1^2. This is only possible when the Pell equation x^2-Dy^2=-1 (1) is solvable. Then ...

A transformation in which coordinates in two spaces are expressed rationally in terms of those in another.

If the total group of the canonical series is divided into two parts, the difference between the number of points in each part and the double of the dimension of the complete ...

A point v is a central point of a graph if the eccentricity of the point equals the graph radius. The set of all central points is called the graph center.

Chain equivalences give an equivalence relation on the space of chain homomorphisms. Two chain complexes are chain equivalent if there are chain maps phi:C_*->D_* and ...

A compact manifold without boundary.

In mathematics, the term "collection" is generally used to mean a multiset, i.e., a set in which order is ignored but multiplicity is significant.

A set U has compact closure if its set closure is compact. Typically, compact closure is equivalent to the condition that U is bounded.