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The pseudo-tangent cone P_S(x) of a subset S subset R^n at a point x in S is the set P_S(x)=convK_S^_, where K_S is the contingent cone of S and where conv(A) is the smallest ...

A set containing all elements of a smaller set. If B is a subset of A, then A is a superset of B, written A superset= B. If A is a proper superset of B, this is written A ...

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 ...

An existential sentence is a statement claiming the existence of an object with given properties. In the language of set theory it can be formulated as follows, exists x in U ...

The Schröder-Bernstein theorem for numbers states that if n<=m<=n, then m=n. For sets, the theorem states that if there are injections of the set A into the set B and of B ...

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 ...

An abstract vector space of dimension n over a field k is the set of all formal expressions a_1v_1+a_2v_2+...+a_nv_n, (1) where {v_1,v_2,...,v_n} is a given set of n objects ...

The above topological structure, composed of a countable union of compact sets, is called Alexander's horned sphere. It is homeomorphic with the ball B^3, and its boundary is ...

In discrete percolation theory, bond percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice graph ...

One of the numbers ..., -2, -1, 0, 1, 2, .... The set of integers forms a ring that is denoted Z. A given integer n may be negative (n in Z^-), nonnegative (n in Z^*), zero ...