Topology and isometries of the de Sitter space-time

Spaces with a constant four-dimensional curvature, which are locally isometric to the de Sitter space-time but differing from it in topology are considered. The de Sitter spaces are considered in coordinates fitted at best for introduction of topology for three cross sections: S3, S1 x S2, S1 x S2 x S3. It is shown that the de Sitter space-time covered by the family of layers, each of them is topologically identical, may be covered by another family of topologically identical layers. But layers in these families will have different topology