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General Theories of Space-Time
We call curves 'World-lines' in space-time.
In the next section we shall have the co-ordination of space-Time as a four-dimensional differentiable manifold with its properties. Co-ordinatization of Space-Time:
Space-Time is a four-dimensional differentible manifold.
Let us characterise its properties. (1) Firstly it is a topology having a point in space-time with
a neighbour say M. (ii) Secondly space-time is co-ordinatizable by R* i.e. set of
four (Quadruplex) real numbers. (iii) Thirdly we define one-one continuous function from the
neighbour M to R* that is illustrated by (iv) Consider a real-valued function defined on a
neighbourhood in space-time. Then we can say is differentiable only if (i.e. apply - the inverse of g) then it is differentiable from into R for every function g.)
Space-Time
l
. <x,(m), x,(m), xz(m), xg(m)>
Ne ghbourhood of R^
M
Co-ordination of Space-Time . (v) Space-Time is a four-dimensional differentiable is purely LOCAL
ASSERTION
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