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A Borel set is an element of a Borel sigma-algebra. Roughly speaking, Borel sets are the sets that can be constructed from open or closed sets by repeatedly taking countable ...

A sigma-algebra which is related to the topology of a set. The Borel sigma-algebra is defined to be the sigma-algebra generated by the open sets (or equivalently, by the ...

A set equipped with a sigma-algebra of subsets.

Let phi(t)=sum_(n=0)^(infty)A_nt^n be any function for which the integral I(x)=int_0^inftye^(-tx)t^pphi(t)dt converges. Then the expansion where Gamma(z) is the gamma ...

The partial differential equation (1-u_t^2)u_(xx)+2u_xu_tu_(xt)-(1+u_x^2)u_(tt)=0.

The Borromean rings, also called the Borromean links (Livingston 1993, p. 10) are three mutually interlocked rings (left figure), named after the Italian Renaissance family ...

The procedure used in subtraction to "borrow" 10 from the next higher digit column in order to obtain a positive difference in the column in question.

Every continuous map f:S^n->R^n must identify a pair of antipodal points.

Borsuk conjectured that it is possible to cut an n-dimensional shape of generalized diameter 1 into n+1 pieces each with diameter smaller than the original. It is true for ...

Use the definition of the q-series (a;q)_n=product_(j=0)^(n-1)(1-aq^j) (1) and define [N; M]=((q^(N-M+1);q)_M)/((q;q)_m). (2) Then P. Borwein has conjectured that (1) the ...