ABSTRACT
Physics deals with observation and measurements of events that occur, be it in nature or in a laboratory experiment, and comparing notes with different observers and drawing conclusions regarding the laws that govern nature. As events occur in space and time, and are measured by any observer by identifying the location of the event and the time of occurrence, in order to represent the event, one requires four numbers identifying the space and time coordinates of the event. This requires a mathematical structure on which all the events can be identified as seen by different observers and be able to link different observers with one another for comparing their notes. Such a structure which can support unique definitions of frames of references of different observers in general is called in general a manifold. In order to define a manifold, one requires several basic concepts like set, function or mapping, continuity, and differentiability, topology, and morphisms which are explained in standard references ([14],[3],[13]), and can be referred to.The frame of reference, mentioned above, needs the notion of a coordinate chart which will be defined below.
