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We find all the higher dimensional solutions of the Einstein-Maxwell theorythat are the topological product of two manifolds of constant curvature. Thesesolutions include the higher dimensional Nariai, Bertotti-Robinson andanti-Nariai solutions, and the anti-de Sitter Bertotti-Robinson solutions withtoroidal and hyperbolic topology (Plebanski-Hacyan solutions). We give explicitresults for any dimension D>3. These solutions are generated from theappropriate extremal limits of the higher dimensional near-extreme black holesin a de Sitter, and anti-de Sitter backgrounds. Thus, we also find the mass andthe charge parameters of the higher dimensional extreme black holes as afunction of the radius of the degenerate horizon.Comment: 10 pages, 11 figures, RevTeX4. References added. Published versio

Nariai, Bertotti-Robinson, and anti-Nariai solutions in higher dimensions