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A metric space X which is not complete has a Cauchy sequence which does not converge. The completion of X is obtained by adding the limits to the Cauchy sequences. For ...

The elongated dodecahedron, also known as the extended rhombic dodecahedron and rhombo-hexagonal dodecahedron, is a space-filling polyhedron and primary parallelohedron ...

The equilateral elongated square dipyramid, illustrated above together with its net, is Johnson solid J_(15). A version of the elongated square dipyramid that is "squashed" ...

A hexagonal prism is a prism composed of two hexagonal bases and six rectangular sides. It is an octahedron. The regular right hexagonal prism is a space-filling polyhedron. ...

A topology tau on a topological vector space X=(X,tau) (with X usually assumed to be T2) is said to be locally convex if tau admits a local base at 0 consisting of balanced, ...

The Lorentz group is the group L of time-preserving linear isometries of Minkowski space R^((3,1)) with the Minkowski metric dtau^2=-(dx^0)^2+(dx^1)^2+(dx^2)^2+(dx^3)^2 ...

The vector space tensor product V tensor W of two group representations of a group G is also a representation of G. An element g of G acts on a basis element v tensor w by ...

A triangular prism is a prism composed of two triangular bases and three rectangular sides. It is a pentahedron. It is implemented in the Wolfram Language as ...

An algebraic manifold is another name for a smooth algebraic variety. It can be covered by coordinate charts so that the transition functions are given by rational functions. ...

A Banach algebra A for which H^1(A,X^*)=Z^1(A,X^*)/B^1(A,X^*)=0 for all Banach A-bimodules X is called amenable (or Johnson amenable; Helemskii 1989, 1997). This notion was ...