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Nana Dutchou

- 14

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(a) The universe U is a topological space whose elements are called events and as each event has a neighborhood homeomorphic to R^4.

(b) A local coordinate system is a homeomorphism between an open subset of U and a bounded subset of R.

(c) A world line segment is a continuous function which is defined on an open subset of R and takes values in U.

(d) A generalized physical space (a set of spatial positions) is a particular family of world lines of material bodies. For example, in general relativity, a generalized physical space of Rindler consists of world lines of a family of Rindler observers. http://en.wikipedia.org/wiki/Rindler_coordinates#The_Rindler_observers

(e) To define a time variable in a generalized physical space we just have to choose a particular parametrization along each of his world lines or (in a corpuscular model) we just have to choose a particular parametrization along the world line of the body whose movement is studied.

*For example, a Poincaré-Einstein dating carried out by an experimenter P is a temporal variable (t) and a Poincaré-Einstein dating carried out by an experimenter P' is another temporal variable (t'). A Poincaré-Einstein dating carried out by an experimenter P is a temporal variable obtained by this method : the date associated with an event A is the arithmetic mean of the dates of issuance and receipt by P of a light signal which is reflected in A.*

**These definitions are correct in general relativity ?**

**Thank you.**Rommel Nana Dutchou