Lineability, spaceability, and additivity cardinals for Darboux-like functions

We introduce the concept of maximal lineability cardinal number, mL(M), of a subset M of a topological vector space and study its relation to the cardinal numbers known as: additivity A(M), homogeneous lineability HL(M), and lineability L(M) of M. In particular, we will describe, in terms of L, the lineability and spaceability of the families of the following Darboux-like functions on R-n, n >= 1: extendable, Jones, and almost continuous function

A result related to the problem CN of Fremlin

We show that the set of injective functions from any uncountable cardinal less than the continuum into the real numbers is of second category in the box product topology

Integrals of a C-1-compatible triangular surface element

Definite integrals are evaluated for the cardinal functions of an interpolation method which provides C sup 1 continuity over a triangular grid

Chebyshev interpolation for functions with endpoint singularities via exponential and double-exponential transforms

We present five theorems concerning the asymptotic convergence rates of Chebyshev interpolation applied to functions transplanted to either a semi-infinite or an infinite interval under exponential or double-exponential transformations. This strategy is useful for approximating and computing with functions that are analytic apart from endpoint singularities. The use of Chebyshev polynomials instead of the more commonly used cardinal sinc or Fourier interpolants is important because it enables one to apply maps to semi-infinite intervals for functions which have only a single endpoint singularity. In such cases, this leads to significantly improved convergence rates