I'm trying to comprehend the discussion here about the internal energy of an ideal gas being only dependant to its temperature $dU=nc_vdT$. I have the feeling that there are some assumptions missing.
What I see from the proofs, for example here, is that they assume they can substitute any thermodynamic process with other incremental processes as far as the consequent process has the same start-end. To understand better what I'm talking about you may consider the conservatives forces where the total work done by the force is independent from the path.
So my question is that if all thermodynamic process with the same start-end are homeomorphic? meaning that this is an intrinsic feature of a thermodynamic system. Or there are certain assumptions to be met? for example has reversibility anything to do here?