We report simultaneous hydrostatic pressure studies on the critical temperature $T_c$ and on the pseudogap temperature $T^*$ performed through resistivity measurements on an optimally doped high-$T_c$ oxide $Hg_{0.82}Re_{0.18}Ba_2Ca_2Cu_3O_{8+delta}$. The resistivity is measured as function of the temperature for several different applied pressure below 1GPa. We find that both $T_c$ and $T^*$ increases linearly with the pressure. This result demonstrate that the well known intrinsic pressure effect on $T_c$ is also present at $T^*$ and both temperatures are originated by the same superconducting mechanism.
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