Abstract. Contrary to a natural expectation, there exist locally homogeneous spaces which are not locally isometric to any (globally) homogeneous spaces. Such examples were found by Kowalski. In this paper we try to understand these mysterious examples well. We denote by $\Cal {LH}(n)$ the set of local isometry classes of $n$-dimensional locally homogeneous spaces. We can introduce the topology on $\Cal {LH}(n)$ by imbedding it in the space of abstract curvature tensors and covariant derivatives. We show that the set of local isometry classes of $n$-dimensional locally homogeneous spaces which are locally isometric to homogeneous spaces are dense in $\Cal {LH}(n)$.
AMSclassification. 53C30, 53B20
Keywords. Locally homogeneous spaces, infinitesimally homogeneous spaces