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The term Bol loop refers to either of two classes of algebraic loops satisfying the so-called Bol identities. In particular, a left Bol loop is an algebraic loop L which, for ...

A C^infty function is a function that is differentiable for all degrees of differentiation. For instance, f(x)=e^(2x) (left figure above) is C^infty because its nth ...

A theorem about (or providing an equivalent definition of) compact sets, originally due to Georg Cantor. Given a decreasing sequence of bounded nonempty closed sets C_1 ...

A Cayley tree is a tree in which each non-leaf graph vertex has a constant number of branches n is called an n-Cayley tree. 2-Cayley trees are path graphs. The unique ...

A surface which is simultaneously complete and minimal. There have been a large number of fundamental breakthroughs in the study of such surfaces in recent years, and they ...

The connected sum M_1#M_2 of n-manifolds M_1 and M_2 is formed by deleting the interiors of n-balls B_i^n in M_i^n and attaching the resulting punctured manifolds M_i-B^._i ...

A differential k-form omega of degree p in an exterior algebra ^ V is decomposable if there exist p one-forms alpha_i such that omega=alpha_1 ^ ... ^ alpha_p, (1) where alpha ...

Given a polygon with an even number of sides, the derived polygon is obtained by joining the points which are a fractional distance r along each side. If r=1/2, then the ...

A factorion is an integer which is equal to the sum of factorials of its digits. There are exactly four such numbers: 1 = 1! (1) 2 = 2! (2) 145 = 1!+4!+5! (3) 40585 = ...

A fallacy is an incorrect result arrived at by apparently correct, though actually specious reasoning. The great Greek geometer Euclid wrote an entire book on geometric ...