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A set in a Polish space is a Borel set iff it is both analytic and coanalytic. For subsets of w, a set is delta_1^1 iff it is "hyperarithmetic."

A topological space fulfilling the T_4-axiom: X fulfils the T1-separation axiom and is normal. In the terminology of Alexandroff and Hopf (1972), T_4-space are called Tietze ...

An abstract manifold is a manifold in the context of an abstract space with no particular embedding, or representation in mind. It is a topological space with an atlas of ...

A basis vector in an n-dimensional vector space is one of any chosen set of n vectors in the space forming a vector basis, i.e., having the property that every vector in the ...

The Gauss map is a function N from an oriented surface M in Euclidean space R^3 to the unit sphere in R^3. It associates to every point on the surface its oriented unit ...

The 11-cell is a regular 4-dimensional structure that cannot be represented in 3-dimensional space in any reasonable way and is highly self-intersecting even in 4-dimensional ...

A vector is formally defined as an element of a vector space. In the commonly encountered vector space R^n (i.e., Euclidean n-space), a vector is given by n coordinates and ...

Every smooth manifold M has a tangent bundle TM, which consists of the tangent space TM_p at all points p in M. Since a tangent space TM_p is the set of all tangent vectors ...

On a measure space X, the set of square integrable L2-functions is an L^2-space. Taken together with the L2-inner product with respect to a measure mu, <f,g>=int_Xfgdmu (1) ...

A Hilbert basis for the vector space of square summable sequences (a_n)=a_1, a_2, ... is given by the standard basis e_i, where e_i=delta_(in), with delta_(in) the Kronecker ...