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A topological space that contains a homeomorphic image of every topological space of a certain class. A metric space U is said to be universal for a family of metric spaces M ...

Suppose that X is a vector space over the field of complex or real numbers. Then the set of all linear functionals on X forms a vector space called the algebraic conjugate ...

Given a topological vector space X and a neighborhood V of 0 in X, the polar K=K(V) of V is defined to be the set K(V)={Lambda in X^*:|Lambdax|<=1 for every x in V} and where ...

The vector space generated by the columns of a matrix viewed as vectors. The column space of an n×m matrix A with real entries is a subspace generated by m elements of R^n, ...

The projective plane crossing number of a graph is the minimal number of crossings with which the graph can be drawn on the real projective plane. A graph with projective ...

The set R union {infty}, obtained by adjoining one improper element to the set R of real numbers, is the set of projectively extended real numbers. Although notation is not ...

A Hilbert space is a vector space H with an inner product <f,g> such that the norm defined by |f|=sqrt(<f,f>) turns H into a complete metric space. If the metric defined by ...

The two-dimensional space consisting of the set of triples {(a,b,c):a,b,c in K, not all zero}, where triples which are scalar multiples of each other are identified.

The dual vector space to a real vector space V is the vector space of linear functions f:V->R, denoted V^*. In the dual of a complex vector space, the linear functions take ...

A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...