Axiomatics of the Observer Manifold and Relativity

We show that Special and General Relativity lead to the introduction of an observer manifold, in addition usual event manifold. Axiomatics require manifolds be Hausdorff are not appropriate for propose alternative axiomatics how most local computations extend this framework without difficulty. The derivation Lorentz transformation takes a new meaning context, enabling identification representations several observers hence reducing manifold However, we example relevant radiation accelerated electrons is always correct. This appears any situation where gravitational fields remote locations have measured on Earth, such as detection waves, or when high accelerations involved, electron laser cooling.