%0 Journal Article
%A Gámez Merino, José Luis
%A Muñoz-Fernández, Gustavo A.
%A Pellegrino, Daniel
%A Seoane Sepúlveda, Juan Benigno
%T Bounded and unbounded polynomials and multilinear forms: Characterizing continuity
%D 2012
%@ 0024-3795
%U https://hdl.handle.net/20.500.14352/42358
%X In 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 as to whether a polynomial is continuous if and only jilt transforms connected sets into connected sets. These results motivate the natural question as to how many non-continuous polynomials there are on an infinite dimensional normed space. A problem on the lineability of the sets of non-continuous polynomials and multilinear mappings on infinite dimensional normed spaces is answered.
%~