Boolean algebras and uniform convergence of series

Uniform convergence of hypergeometric series

The considered problem is uniform convergence of sequences of hypergeometric series. We give necessary and sufficient conditions for uniformly dominated convergence of infinite sums of proper bivariate hypergeometric terms. These conditions can be checked algorithmically. Hence the results can be applied in Zeilberger type algorithms for nonterminating hypergeometric series.

Uniform Convergence of Double Trigonometric Series

It is a classical problem in Fourier analysis to give conditions for a single sine or cosine series to be uniformly convergent. Several authors gave conditions for this problem supposing that the coefficients are monotone, non-negative or more recently, general monotone. There are also results for the regular convergence of double sine series to be uniform in case the coefficients are monotone ...

Uniform convergence of single and double sine series and integrals

Some Forcing Related Convergence Structures on Complete Boolean Algebras

Let convergences λi : B → P (B), i ≤ 4, on a complete Boolean algebra B be defined in the following way. For a sequence x = 〈xn : n ∈ ω〉 in B and the corresponding B-name for a subset of ω, τx = {〈ň, xn〉 : n ∈ ω}, let λi(x) = { {‖τx is infinite‖} if bi(x) = 1B, ∅ otherwise, where b1(x) = ‖τx is finite or cofinite‖, b2(x) = ‖τx is not unsupported‖, b3(x) = ‖τx is not a splitting real‖ and b4(x) ...

Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...