Construction of Hartman-Mycielski and separation axioms on semitopological groups.

The construction of Hartman-Mycielski consists of associating every topological group with a pathwise connected and locally pathwise connected topological group and such that can be embedded as a closed subgroup into . It is known that both topological groups share many interesting properties. This construction was originally thought for topological groups and now we are studying it in semitopological groups. When we go from a topological group to a semitopological group we find significant differences in the behavior of properties such as axioms of separation, cardinal functions and symmetry-like properties. Also, if we study semitopological and paratopological groups we can find important differences in the behavior of some separation axioms. The goal of this talk is to present some of the most important separation axioms that are shared between and when is a semitopological (paratopological) group.