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The (lower) domination number gamma(G) of a graph G is the minimum size of a dominating set of vertices in G, i.e., the size of a minimum dominating set. This is equivalent ...

An edge cut (Holton and Sheehan 1993, p. 14; West 2000, p. 152), edge cut set, edge cutset (Holton and Sheehan 1993, p. 14), or sometimes simply "cut set" or "cutset" (e.g., ...

The underlying set of the fundamental group of X is the set of based homotopy classes from the circle to X, denoted [S^1,X]. For general spaces X and Y, there is no natural ...

A set function mu is said to possess finite subadditivity if, given any finite disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) ...

Let H be a Hilbert space and (e_i)_(i in I) an orthonormal basis for H. The set of all products of two Hilbert-Schmidt operators is denoted N(H), and its elements are called ...

The Lebesgue measure is an extension of the classical notions of length and area to more complicated sets. Given an open set S=sum_(k)(a_k,b_k) containing disjoint intervals, ...

The axiom of Zermelo-Fraenkel set theory which asserts the existence of a set containing all the natural numbers, exists x(emptyset in x ^ forall y in x(y^' in x)), where ...

A notation is a set of well-defined rules for representing quantities and operations with symbols.

In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3, .... In formal set theory, a cardinal number (also called "the ...