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A covariant tensor, denoted with a lowered index (e.g., a_mu) is a tensor having specific transformation properties. In general, these transformation properties differ from ...

The taxicab metric, also called the Manhattan distance, is the metric of the Euclidean plane defined by g((x_1,y_1),(x_2,y_2))=|x_1-x_2|+|y_1-y_2|, for all points ...

A topological space is second countable if it has a countable topological basis.

A complete metric is a metric in which every Cauchy sequence is convergent. A topological space with a complete metric is called a complete metric space.

The vectors +/-a_1, ..., +/-a_n in a three-space form a normalized eutactic star iff Tx=x for all x in the three-space.

Let z_0 be a point in a simply connected region R!=C, where C is the complex plane. Then there is a unique analytic function w=f(z) mapping R one-to-one onto the disk |w|<1 ...

The only irreducible spherical simplexes generated by reflection are A_n (n>=1), B_n (n>=4), C_n (n>=2), D_2^p (p>=5), E_6, E_7, E_8, F_4, G_3, and G_4. The only irreducible ...

The term cube is used in topology to denote the Cartesian product of any (finite or infinite) number of copies of the closed interval [0,1] equipped with the product topology ...

A graded algebra over the integers Z. Cohomology of a space is a graded ring.

A smooth manifold with a Poisson bracket defined on its function space.