%0 Journal Article %A Martínez Ansemil, José María %A López-Salazar Codes, Jerónimo %A Ponte Miramontes, María Del Socorro %T On real analytic functions of unbounded type. %D 2013 %@ 1139-1138 %U https://hdl.handle.net/20.500.14352/33332 %X In this paper we prove several results on the existence of analytic functions on an infinite dimensional real Banach space which are bounded on some given collection of open sets and unbounded on others. In addition, we also obtain results on the density of some subsets of the space of all analytic functions for natural locally convex topologies on this space %~