Martínez Ansemil, José MaríaPonte Miramontes, María Del SocorroLópez-Salazar Codes, Jerónimo2023-06-192023-06-192015Martínez Ansemil, J. M., Ponte Miramontes, M. S. & López-Salazar Codes, J. «The Spaces of Analytic Functions on Open Subsets of $\mathbb R^{\mathbb N}$ and $\mathbb C^{\mathbb N}$». Publications of the Research Institute for Mathematical Sciences, vol. 51, n.o 1, abril de 2015, pp. 191-206. DOI.org (Crossref), https://doi.org/10.4171/prims/152.0034-531810.4171/PRIMS/152https://hdl.handle.net/20.500.14352/34661This 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.journal articlehttps//doi.org/10.4171/PRIMS/152https://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=51&iss=1&rank=5metadata only access51Analytic functionLocally convex topologyInductive limitMatemáticas (Matemáticas)12 Matemáticas