Now showing items 1-9 of 9
Nowhere hölderian functions and Pringsheim singular functions in the disc algebra [Article]
We prove the existence of dense linear subspaces, of infinitely generated subalgebras and of infinite dimensional Banach spaces in the disc algebra all of whose nonzero members are not α-h¨olderian at any point of the ...
Lineability and modes of convergence [Article]
In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are ...
The set of space-filling curves: topological and algebraic structure [Article]
In this paper, a study of topological and algebraic properties of two families of functions from the unit interval I into the plane R2 is performed. The first family is the collection of all Peano curves, that is, of those ...
Algebraic structure of continuous, unbounded and integrable functions [Article]
In this paper we study the large linear and algebraic size of the family of unbounded continuous and integrable functions in [0, +∞) and of the family of sequences of these functions converging to zero uniformly on ...
Hausdorff and Box dimensions of continuous functions and lineability [Article]
(Taylor & Francis, 2019-05)
Given s ∈ (1, 2], we study (among other questions) the algebraic genericity of the set of continuous functions f : [0, 1] → R whose graph has Hausdorff (or Box) dimension exactly s.
Linear subsets of nonlinear sets in topological vector spaces [Article]
(American Mathematical Society, 2014-01)
For the last decade there has been a generalized trend in Mathematics on the search for large algebraic structures (linear spaces, closed subspaces, or infinitely generated algebras) composed of mathematical objects enjoying ...
Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces [Article]
We prove in this paper the existence of dense linear subspaces in the classical holomorphic Lipschitz spaces in the disc all of whose non-null functions are nowhere differentiable at the boundary. Infinitely generated free ...
Structural aspects of the non-uniformly continuous functions and the unbounded functions within C(X) [Article]
We prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then, under appropriate mild assumptions, there exists in fact a plethora of such functions, in both ...
Large algebras of singular functions vanishing on prescribed sets [Article]
In this paper, the non-vacuousness of the family of all nowhere analytic infinitely differentiable functions on the real line vanishing on a prescribed set Z is characterized in terms of Z. In this case, large algebraic ...