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The aim of this paper is to generalize the hyperplane section theorem ofGurjar to arbitrary (local) analytic varieties even if the intersection with ofhyperplanes is not necessarily isolated.  In case of formal varieties, we generalize the statement to work fordifferent classes of functions than just hyperplanes. We call these classes(which are subsets of formal power series ring) to be algebraic$\mathbb{m}$-adicaly closed (A$\mathbb{m}$AC).

Generalization of Gurjar's Hyperplane section theorem to arbitrary analytic varieties and A$\mathbb{m}$AC classes