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A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set ...

Wang's conjecture states that if a set of tiles can tile the plane, then they can always be arranged to do so periodically (Wang 1961). The conjecture was refuted when Berger ...

A set of sample problems in unconstrained optimization is given by loading Optimization`UnconstrainedProblems` and evaluating $FindMinimumProblems.

Let S be a nonempty set of real numbers that has a lower bound. A number c is the called the greatest lower bound (or the infimum, denoted infS) for S iff it satisfies the ...

Let S be a nonempty set of real numbers that has an upper bound. Then a number c is called the least upper bound (or the supremum, denoted supS) for S iff it satisfies the ...

A sorting algorithm which makes n passes over a set of n elements, in each pass selecting the smallest element and deleting it from the set. This algorithm has running time ...

The transitive reflexive reduction of a partial order. An element z of a partially ordered set (X,<=) covers another element x provided that there exists no third element y ...

Proper covers are defined as covers of a set X which do not contain the entire set X itself as a subset (Macula 1994). Of the five covers of {1,2}, namely {{1},{2}}, {{1,2}}, ...

The maximum flow between vertices v_i and v_j in a graph G is exactly the weight of the smallest set of edges to disconnect G with v_i and v_j in different components (Ford ...

Let L=(L, ^ , v ) be a lattice, and let f,g:L->L. Then the pair (f,g) is a local polarity if and only if for each finite set X subset= L, there is a finitely generated ...