%0 Journal Article
%T On extension of partial orders to total preorders with prescribed symmetric part
%A Dmitry V. Akopian
%A Valentin V. Gorokhovik
%J Mathematics
%D 2011
%I arXiv
%X For a partial order $\preceq$ on a set X and an equivalency relation S defined on the same set X we derive a necessary and sufficient condition for the existence of such a total preorder on X whose asymmetric part contains the asymmetric part of the given partial order $\preceq$ and whose symmetric part coincides with the given equivalence relation S. This result generalizes the classical Szpilrajn theorem on extension of a partial order to a perfect (linear) order.
%U http://arxiv.org/abs/1111.1390v1