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Complete digraphs are digraphs in which every pair of nodes is connected by a bidirectional edge.

If a sphere is covered by three closed sets, then one of them must contain a pair of antipodal points.

Somewhere on the Earth, there is a pair of antipodal points having simultaneously the same temperature and pressure.

The space join of a topological space X and a pair of points S^0, Sigma(X)=X*S^0.

A solitary number is a number which does not have any friends. Solitary numbers include all primes, prime powers, and numbers for which (n,sigma(n))=1, where (a,b) is the ...

If two pairs of opposite polygon vertices of a complete quadrilateral are pairs of harmonic conjugate points, then the third pair of opposite polygon vertices is likewise a ...

If two intersections of each pair of three conics S_1, S_2, and S_3 lie on a conic S_0, then the lines joining the other two intersections of each pair are concurrent (Evelyn ...

A pair of overdots placed over a symbol, as in x^.., most commonly used to denote a second derivative with respect to time, i.e., x^..=d^2x/dt^2.

A theory which satisfies all the Eilenberg-Steenrod axioms with the possible exception of the long exact sequence of a pair axiom, as well as a certain additional continuity ...

A set in R^d is concave if it does not contain all the line segments connecting any pair of its points. If the set does contain all the line segments, it is called convex.