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Let S be a collection of subsets of a set X, mu:S->[0,infty] a set function, and mu^* the outer measure induced by mu. The measure mu^_ that is the restriction of mu^* to the ...

A sigma-algebra which is related to the topology of a set. The Borel sigma-algebra is defined to be the sigma-algebra generated by the open sets (or equivalently, by the ...

Integer programming in a special case of linear programming in which all variables are required to take on integer values only. Set covering deployment is an example ...

If T is a set of axioms in a first-order language, and a statement p holds for any structure M satisfying T, then p can be formally deduced from T in some appropriately ...

Sea horse valley is a name sometimes given to the portion of the Mandelbrot set centered around -0.75+0.1i.

Let A be a set. An operation on A is a function from a power of A into A. More precisely, given an ordinal number alpha, a function from A^alpha into A is an alpha-ary ...

Let S be a nonempty set, then an ultrafilter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F. 2. If A,B in F, then A ...

In common usage, an ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc. In formal set theory, an ordinal ...

The set of all zero-systems of a group G is denoted B(G) and is called the block monoid of G since it forms a commutative monoid under the operation of zero-system addition ...

Let P be a finite partially ordered set. A chain in P is a set of pairwise comparable elements (i.e., a totally ordered subset). The partial order length of P is the maximum ...