uncountable n-tuplets?

It seems that a lot of topological constructions can represent some
kind of "number". For example, [0,1) x N represents the Reals. And RxR
represents the complex plane. There are all sorts of very useful
mathematics that come from using the complex plane. Has anyone ever
tried treating numbers as anything more? For example, what about
triplets, like (x,y,z). Or quadruplets?

Or why not an infinite tuplet.. (x,y,z........ etc).

How about an uncountable tuplet? Something like there is a tuplet for
each Real.

There is also the Long Line, which is [0,1)xR. Let's call that L. Can
you have "long complex numbers" on a plane that is L x L?

Sorry if these are dumb questions, I was just wondering.. it seems like
there is some kind of useful algebra for treating numbers in all kinds
of forms, like tuplets, and matrices... so why not any of the above?

Julien

.

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