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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 class of continuous functions is called the Baire class 0. For each n, the functions that can be considered as pointwise limits of sequences of functions of Baire class ...

A topological space X in which each subset of X of the "first category" has an empty interior. A topological space which is homeomorphic to a complete metric space is a Baire ...

A procedure for finding the quadratic factors for the complex conjugate roots of a polynomial P(x) with real coefficients. (1) Now write the original polynomial as ...

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 number 13.

The map x_(n+1)=2mux_n, (1) where x is computed modulo 1. A generalized Baker's map can be defined as x_(n+1) = {lambda_ax_n y_n<alpha ; (1-lambda_b)+lambda_bx_n y_n>alpha ...

The Balaban 10-cage is one of the three (3,10)-cage graphs (Read and Wilson 1998, p. 272). The Balaban (3,10)-cage was the first known example of a 10-cage (Balaban 1973, ...

The Balaban 11-cage is the unique 11-cage graph, derived via a tree excision from the 12-cage graph by Balaban (1973) and proven unique by McKay and Myrvold in 2003. It is ...

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 ...