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A product space product_(i in I)X_i is compact iff X_i is compact for all i in I. In other words, the topological product of any number of compact spaces is compact. In ...

Let gamma(G) denote the domination number of a simple graph G. Then Vizing (1963) conjectured that gamma(G)gamma(H)<=gamma(G×H), where G×H is the graph product. While the ...

Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that ...

A set A in a first-countable space is dense in B if B=A union L, where L is the set of limit points of A. For example, the rational numbers are dense in the reals. In ...

For a nonzero real number r and a triangle DeltaABC, swing line segment BC about the vertex B towards vertex A through an angle rB. Call the line along the rotated segment L. ...

A real quantity having a value less than zero (<0) is said to be negative. Negative numbers are denoted with a minus sign preceding the corresponding positive number, i.e., ...

The anticomplementary triangle is the triangle DeltaA_1^'A_2^'A_3^' which has a given triangle DeltaA_1A_2A_3 as its medial triangle. It is therefore the anticevian triangle ...

An operator which describes the time evolution of densities in phase space. The operator can be defined by rho_(n+1)=L^~rho_n, where rho_n are the natural invariants after ...

The summatory function Phi(n) of the totient function phi(n) is defined by Phi(n) = sum_(k=1)^(n)phi(k) (1) = sum_(m=1)^(n)msum_(d|m)(mu(d))/d (2) = ...

Let F be a differential field with constant field K. For f in F, suppose that the equation g^'=f (i.e., g=intf) has a solution g in G, where G is an elementary extension of F ...