  We show that every affine or projective algebraic variety defined over the
field of real or complex numbers is homeomorphic to a variety defined over the
field of algebraic numbers. We construct such a homeomorphism by choosing a
small deformation of the coefficients of the original equations. This method is
based on the properties of Zariski equisingular families of varieties.
  Moreover we construct an algorithm, that, given a system of equations
defining a variety $V$, produces a system of equations with algebraic
coefficients of a variety homeomorphic to $V$
