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Recently, it has been proved that, assuming that there is an almost disjoint family of cardinality 2(c) in c (which is assured, for instance, by either Martin's Axiom, or the Continuum Hypothesis, or even 2(texto impreso
Gámez Merino, José Luis ; Muñoz-Fernández, Gustavo A. ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. | Elsevier Science | 2012-01In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the question a[...]texto impreso
Ciesielski, Krzysztof Chris ; Gámez Merino, José Luis ; Mazza, L. ; Seoane-Sepúlveda, Juan B. | American Mathematical Society | 2017We investigate the additivity A and lineability L cardinal coeffiients for the following classes of functions: ES\SES of everywhere surjective functions that are not strongly everywhere surjective, Darboux-like, Sierpinski-Zygmund, surjective, a[...]texto impreso
Gámez Merino, José Luis ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Mathematical Assoc Amer | 2011-02It is well known that a function f : R -> R is continuous if and only if the image of every compact set under f is compact and the image of every connected set is connected. We show that there exist two 2(c)-dimensional linear spaces of nowhere[...]texto impreso
Fenoy, Mar ; Gámez Merino, José Luis ; Muñoz-Fernández, Gustavo A. ; Sáez Maestro, Eva | De Gruyter Open Ltd | 2017This expository paper focuses on the study of extreme surjective functions in ??. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the[...]texto impreso
In this paper the author studies large linear structures inside the set of Jones functions. He shows that there is an infinite-dimensional linear space inside this set. Further, the linear space is isomorphic to RR, so it is as large as possible[...]texto impreso
We give a condition for a family of functions to be lineable by means of its additivity. The novelty presented here is that we solve the lineability problem using a technique that is not constructive, as are most approaches to this problem. We r[...]texto impreso
Ciesielski, Krzysztof Chris ; Gámez Merino, José Luis ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. | Elsevier Science | 2014-01-01We 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 [...]texto impreso
The two main results of this paper are the following: (a) If X is a Banach space and f : [a, b] --> X is a function such that x*f is Denjoy integrable for all x* is an element of X*, then f is Denjoy-Dunford integrable, and (b) There exists a D[...]texto impreso
Gámez Merino, José Luis ; Muñoz-Fernández, Gustavo A. ; Sánchez, V.M. ; Seoane-Sepúlveda, Juan B. | American Mathematical Society | 2010-11We find large algebraic structures inside the following sets of pathological functions: (i) perfectly everywhere surjective functions, (ii) differentiable functions with almost nowhere continuous derivatives, (iii) differentiable nowhere monoton[...]
