LAUSR

Abstract In this paper, the authors introduce and study the notions of symmetrically connected extension and antisymmetrically connected extension for T 0 -quasi-metric spaces which satisfy some special conditions, with the help of two types of connectedness, described in the sense of asymmetric topology. In particular, the facts that each bounded T 0 -quasi-metric space has a symmetrically connected one-point extension and each metric space has an antisymmetrically connected one-point extension are proved. Also, several observations on some specific examples of symmetrically connected T 0 -quasi-metric extensions are presented in relation to the connectedness of the graphs, in the sense of graph theory. Furthermore, in order to give some answers for the natural question whether each T 0 -quasi-metric space has a one-point antisymmetrically connected extension or not, we prove some stronger results for the antisymmetrically connected extensions, by describing a weaker notion which is a generalization of boundedness.