Physical properties of the ideal Bose gas with non-integer dimensions between D = 2 and D = 3 are theoretically investigated. Calculation shows that there exists a hierarchy of condensation transitions with changing fractional dimensionality. The results obtained on the specific heat and the condensed density in non-integer dimensions are similar to those for liquid helium-4 in porous media. This results suggest that the geometrical factor may be important for the physical properties of liquid helium-4 in porous media.