We prove that for every homogeneous and strongly locally homogeneous Polish space X there is a Polish group admitting a transitive action on X. We also construct an example of a homogeneous Polish space which is not a coset space and on which no separable metrizable topological group acts transitively.

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

In this paper we investigate the canonical structure of diffeomorphism invariant phase spaces for spatially locally homogeneous spacetimes with 3-dimensional compact closed spaces. After giving a general algorithm to express the diffeomorphisminvariant phase space and the canonical structure of a locally homogeneous system in terms of those of a homogeneous system on a covering space and a modu...

In this paper we investigate the canonical structure of diffeomorphism invariant phase spaces for spatially locally homogeneous spacetimes with 3-dimensional compact closed spaces. After giving a general algorithm to express the diffeomorphisminvariant phase space and the canonical structure of a locally homogeneous system in terms of those of a homogeneous system on a covering space and a modu...

Let M be a family of subspaces of a metric space X. The space X is M–homogeneous if any isometry between two subspaces in M can be extended to an isometry of X. In the case when M is the family of all subspaces of X, the space X is said to be fully homogeneous. We show that the space L, where L is a fully homogeneous subspace of R, is R– homogeneous where R is the family of subspaces that are p...