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Baire's category theorem, also known as Baire's theorem and the category theorem, is a result in analysis and set theory which roughly states that in certain spaces, the ...

The series z=ln(e^xe^y) (1) for noncommuting variables x and y. The first few terms are z_1 = x+y (2) z_2 = 1/2(xy-yx) (3) z_3 = 1/(12)(x^2y+xy^2-2xyx+y^2x+yx^2-2yxy) (4) z_4 ...

The Balaban index J is a graph index defined for a graph on n nodes, m edges, and c connected components by J=m/(gamma+1)sum_((i,j) in E(G))(D_iD_j)^(-1/2), where gamma=m-n+c ...

The Banach-Steinhaus theorem is a result in the field of functional analysis which relates the "size" of a certain subset of points defined relative to a family of linear ...

A Banach space is a complete vector space B with a norm ||·||. Two norms ||·||_((1)) and ||·||_((2)) are called equivalent if they give the same topology, which is equivalent ...

A band over a fixed topological space X is represented by a cover X= union U_alpha, U_alpha subset= X, and for each alpha, a sheaf of groups K_alpha on U_alpha along with ...

The Barnes-Wall lattice is a d-dimensional lattice that exists when d is a power of 2. It is implemented in the Wolfram Language as LatticeData[{"BarnesWall", n}]. Special ...

Barnette's conjecture asserts that every 3-connected bipartite cubic planar graph is Hamiltonian. The only graph on nine or fewer vertices satisfying Barnette's conditions is ...

A barrel solid of revolution composed of parallel circular top and bottom with a common axis and a side formed by a smooth curve symmetrical about the midplane. The term also ...

A pair of identical plane regions (mirror symmetric about two perpendicular lines through the center) which can be stitched together to form a baseball (or tennis ball). A ...