could someone show me some subspaces of R^3 and some convergent sequences here.
note:we study on only bounded spaces.
thanks

could someone show me some subspaces of R^3 and some convergent sequences here.
note:we study on only bounded spaces.
thanks
When you say bounded spaces, do you mean the space is closed under some operation?
Hmm... Is mathematical nomenclature undergoing some linguistic drift?
Anyhow; http://www.math.jhu.edu/~nitu/subspace.pdf
to begin with responding your question, no , no such thing.
you remarked closure. and you are probably aware that any subspace is closed.
furthermore,I need some 3D graph and illustrations.(Non linear samples would be better) thanks for your shared post but the document that you provide is very very brief.
I need detailed instructions
Last edited by unknown_artist; December 28th, 2018 at 09:11 AM.
R^3 by its nature is a linear space. Non linear examples in that space would be functions. The subspaces of some R^n would be all R^m such that m<n and m>0. Any vector space with a bound is not closed under either vector addition or scaler multiplication because the result of some operation might be outside the bound.
Try Googling “vector function”.
oh ,sorry for failure. I did not complete my sentence.I was to say ;
"any subspace will be complete when it is closed."
and a question :
can we create functional sequences which their elements are vector function each?
(I am deling with engineering projects and thus,I need examples as much as possible.)
Last edited by unknown_artist; December 28th, 2018 at 12:15 PM.
Well, swimming in the deep water here. (See what I did there?)
Try here; https://en.wikipedia.org/wiki/Vectorvalued_function
“Linear” quite literally references lines. So any function that defines a line is a linear function. In R^2, y=mx+b is a linear function, and any exponential function would define a curve so as to be nonlinear. Not sure here, but I believe that the surface of a sphere is an example of a nonlinear space. Any manifold that has a noneuclidean metric should be a nonlinear space. If a real mathematician should tell you different, then believe them.
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