proposition in the steady state theory that the Universe looks the same everywhere at all times.

The assumption that on a large scale the universe is homogeneous and isotropic in space and unchanging in time.

an assumption that the universe is everywhere uniform and looks the same in any direction in all space and time---it is the same everywhere and does not change throughout time.

The assumption that the mean density of matter in the universe is constant.

The Perfect Cosmological Principle states that the Universe is homogenous and isotropic in space and time. In this view the universe looks the same everywhere (on the large scale) as it always has and always will. It is the principle underpinning steady-state theory.