We give three different descriptions of the $\tau$-precompact Hausdorff group reflection of topological groups. In particular, we describe the $\omega$-narrow Hausdorff reflection of a given topological group. We also prove that the $\tau$-precompact Hausdorff reflection functor preserves perfect surjective homomorphisms, quotient homomorphisms and arbitrary products. As a direct application, we deduce that the compact Hausdorff reflection functor preserves arbitrary products.
"The $\tau$-precompact Hausdorff Group Reflection of Topological Groups." Bull. Belg. Math. Soc. Simon Stevin 25 (1) 107 - 120, march 2018. https://doi.org/10.36045/bbms/1523412056