Local topological algebraicity of analytic function germs
  T. Mostowski showed that every (real or complex) germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that every (real or complex) analytic function germ, defined on a possibly singular analytic space, is topologically equivalent to a polynomial function germ defined on an affine algebraic variety. 
Marcin Bilski, Adam Parusinski, Guillaume Rond
math.AG math.AC math.CV