Now showing items 1-7 of 7
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 ...
Vector spaces of non-extendable holomorphic functions [Article]
In this paper, the linear structure of the family He(G) of holomorphic functions in a domain G of the complex plane that are not analytically continuable beyond the boundary of G is analyzed. We prove that He(G) contains, ...
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 ...
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 ...