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A proper subset S^' of a set S, denoted S^' subset S, is a subset that is strictly contained in S and so necessarily excludes at least one member of S. The empty set is ...

A subgraph G^' of a graph G is a graph G^' whose vertex set and edge set are subsets of those of G. If G^' is a subgraph of G, then G is said to be a supergraph of G^' ...

One of the Zermelo-Fraenkel axioms which asserts the existence for any set a of a set x such that, for any y of a, if there exists a z satisfying A(y,z), then such z exists ...

The total domination number gamma_t of a graph is the size of a smallest total dominating set, where a total dominating set is a set of vertices of the graph such that all ...

A mathematical object (such as a set or function) is said to bounded if it possesses a bound, i.e., a value which all members of the set, functions, etc., are less than.

The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

A set U has compact closure if its set closure is compact. Typically, compact closure is equivalent to the condition that U is bounded.

A set R of linear extensions of a partially ordered set P=(X,<=) is a realizer of P (and is said to realize P) provided that for all x,y in X, x<=y iff x is below y in every ...

A set in R^d formed by translating an affine subspace or by the intersection of a set of hyperplanes.

An infinite set, such as the real numbers, which is not countably infinite.