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X fulfils the T1-separation axiom and is regular. A space satisfying the T_3-separation axiom is said to be a T3-space.

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

The Eulerian number <n; k> gives the number of permutations of {1,2,...,n} having k permutation ascents (Graham et al. 1994, p. 267). Note that a slightly different ...

An n-step Fibonacci sequence {F_k^((n))}_(k=1)^infty is defined by letting F_k^((n))=0 for k<=0, F_1^((n))=F_2^((n))=1, and other terms according to the linear recurrence ...

A dodecagon is a 12-sided polygon. Several special types of dodecagons are illustrated above. In particular, a dodecagon with vertices equally spaced around a circle and with ...

Li and Yorke (1975) proved that any one-dimensional system which exhibits a regular cycle of period three will also display regular cycles of every other length as well as ...

An outer measure mu on R^n is Borel regular if, for each set X subset R^n, there exists a Borel set B superset X such that mu(B)=mu(X). The d-dimensional Hausdorff outer ...

A regular local ring is a local ring R with maximal ideal m so that m can be generated with exactly d elements where d is the Krull dimension of the ring R. Equivalently, R ...

The important binomial theorem states that sum_(k=0)^n(n; k)r^k=(1+r)^n. (1) Consider sums of powers of binomial coefficients a_n^((r)) = sum_(k=0)^(n)(n; k)^r (2) = ...

Closed forms are known for the sums of reciprocals of even-indexed Fibonacci numbers P_F^((e)) = sum_(n=1)^(infty)1/(F_(2n)) (1) = ...