  The paper deals with the problem posed by Katz and Morris whether the free
product with amalgamation of any Hausdorff topological groups is Hausdorff, the
negative solution of which (even for the particular case of a closed
amalgamated subgroup) easily follows from the relevant result by Uspenskij. The
topology of such a product is characterized by proving that it coincides with
the so-called $X_0$-topology in the sense of Mal'tsev for the corresponding
pushout $X$ in the category of Hausdorff topological spaces. Applying this
characterization, it is proved that the canonical mappings of Hausdorff groups
into their amalgamated free product are open homeomorphic embeddings if an
amalgamated subgroup is open. This immediately implies that in that case this
product is Hausdorff.
