ИСТИНА

Strongly locally homogeneous (SLH) spaces were introduced by L.Ford, who proved that they are coset spaces. For metrizable spaces J.~van Mill sharpened this result showing that separable metrizable (Polish) SLH space is a coset space of a separable metrizable (Polish) group. We give characterization of Polish SLH spaces and show that every separable metrizable SLH space has a completion which is a Polish SLH space. Moreover this completion is obtained in agreement with the completion of the group that realizes the SLH property of a SLH space in two-sided uniformity.