  We study the analytic structure of the space of germs of an analytic function
at the origin of \ww C^{\times m} , namely the space \germ{\mathbf{z}} where
\mathbf{z}=\left(z\_{1},\cdots,z\_{m}\right) , equipped with a convenient
locally convex topology. We are particularly interested in studying the
properties of analytic sets of \germ{\mathbf{z}} as defined by the vanishing
locus of analytic maps. While we notice that \germ{\mathbf{z}} is not Baire we
also prove it enjoys the analytic Baire property: the countable union of proper
analytic sets of \germ{\mathbf{z}} has empty interior. This property underlies
a quite natural notion of a generic property of \germ{\mathbf{z}} , for which
we prove some dynamics-related theorems. We also initiate a program to tackle
the task of characterizing glocal objects in some situations.
