Re: SUO: Re: Proposed SUO Content Outline
John,
It seems that your definition of coordinate system below could apply to
anything
that consists of a two sets and a function (okay, maybe a function that
"is (locally at least) one-to-one, continuous, and differentiable") between
them.
As such, is this definition too general, in that it doesn't go far enough
in distinguishing what is special about a coordinate system from other
kinds of things that consist of two sets and a certain kind of function
between them?
At what point of generality should the thing we define as a coordinate system
look different from other things?
Jim
A coordinate system is nothing more nor less than a set C
>called the coordinates, a designated region R of space-time,
>and a function that maps C into points of R. This is true
>of coordinate systems tied to the earth, to the sun, to the
>center of gravity of the universe, or whatever. It is true
>of 4D systems and 3D+time systems. It is true of inertial
>coordinate systems and arbitrarily accelerated systems.