Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Amalgamated free products of topological groups being Hausdorff -- a new
  approach   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.

14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph