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The homeomorphic image of a so-called "complete separable" metric space. The continuous image of a Polish space is called a Souslin set.

One of the symmetry groups of the Platonic solids. There are three polyhedral groups: the tetrahedral group of order 12, the octahedral group of order 24, and the icosahedral ...

A line segment where two faces of a polyhedron meet, also called a side.

If a polynomial P(x) has a root x=a, i.e., if P(a)=0, then x-a is a factor of P(x).

A graph G is called d-polytopal if there exists a d-dimensional convex polytope P such that the vertices and edges of G are in a one-to-one incidence-preserving ...

A one-dimensional line segment where two two-dimensional faces of an n-dimensional polytope meet, also called a side.

A result in control theory. Define H(psi,x,u)=(psi,f(x,u))=sum_(a=0)^npsi_af^a(x,u). Then in order for a control u(t) and a trajectory x(t) to be optimal, it is necessary ...

A quantity x>0, which may be written with an explicit plus sign for emphasis, +x.

Let A and B be C^*-algebras, then a linear map phi:A->B is said to be positive if phi(A_+) subset= B_+. Here, A_+ is denoted the positive part of A. For example, every ...

A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived. The whole of ...