E-MAIL: xcaicedo@uniandes.edu.co

rfisaacs@matematicas.unal.edu.co

risaacs@ciencias.ciencias.unal.edu.co

• ABSTRACT: We associate to each ultrafilter U the equational class of U-algebras, which are sets endowed with an operator in countable many arguments satisfying certain equations induced by the ultrafilter. This variety may be embedded in the category of T₁ and U-compact topological spaces. Many topological spaces are in the image of this embbeding, in particular all U-compact, Hausdorff, first countable spaces. In this special case we prove that the embbeding transforms, respectively, the subalgebras, quotient algebras and countable products in closed subspaces, quotient spaces and countable products.