What is an analytics space? I have seen more definitions, so my question is - what is the version used the most? And is it all the same notion, or can there be confusion regarding more terms with the same name?
Thank you very much for your insights!
Definition 1: Wikipedia An analytic space is a space that is locally the same as an analytic variety. An analytic space is a locally ringed space $(X,{\mathcal {O}}_{X})$ such that around every point $x$ of X, there exists an open neighborhood $U$ such that $(U,{\mathcal {O}}_{U})$ is isomorphic (as locally ringed spaces) to an analytic variety with its structure sheaf. Such an isomorphism is called a local model for $X$ at $x$.
Definition 2: (from Analytic Sets in Locally Convex Spaces)
In general, by an analytic space we shall mean any Cartan space $(X , X^0)$ for which there exists a covering of $X$ by open sets $\Omega_i$ such that the induced spaces $(\Omega_i, O_{\Omega_i})$ are isomorphic to models.