%0 Journal Article
%A Martínez Ansemil, José María
%A Ponte Miramontes, María Del Socorro
%A López-Salazar Codes, Jerónimo
%T The spaces of analytic functions on open subsets of RN and CN
%D 2015
%@ 0034-5318
%U https://hdl.handle.net/20.500.14352/34661
%X This paper is devoted to studying the space A(U) of all analytic functions on an open subset U of ℝℕ or ℂℕ. It is proved that if U satisfies a weak condition (that will be called the 0-property), then every f ϵ A(U) depends only on afinite number of variables. Several topologies on A(U) are then studied: the compact-open topology, the Tδ topology (already known in spaces of holomorphic functions) and a new one, defined by the inductive limit of the subspaces of analytic functions which only depend on a finite number of variables.
%~