• Sep 14th 2009, 09:21 AM
raed
hello ,could u give me examples for:
1.vector space and vector subspaces.
2.metric space and normed space.
3.banach space and hilbert space.
And thanks alot for all.
• Sep 14th 2009, 09:23 AM
arbolis
Quote:

Originally Posted by raed
hello ,could u give me examples for:
1.vector space and vector subspaces.
2.metric space and normed space.
3.banach space and hilbert space.
And thanks alot for all.

I suggest you to do a research in wikipedia first.
Then try to prove that indeed they are vector space or subspace. Ask here for help if you're stuck on proving.
• Sep 14th 2009, 11:09 PM
raed
Quote:

Originally Posted by arbolis
I suggest you to do a research in wikipedia first.
Then try to prove that indeed they are vector space or subspace. Ask here for help if you're stuck on proving.

Thanks for ur opinion but the proofs and examples are very difficult so i hope to find the answer in this forum
• Sep 15th 2009, 03:33 AM
HallsofIvy
Your question is simply too "large". You are really asking for several different courses. We could give examples, but if you don't know what "vector space", "subspace", "Banach space", etc. are just examples won't help you.
• Sep 15th 2009, 09:35 AM
arbolis
Quote:

Originally Posted by raed
Thanks for ur opinion but the proofs and examples are very difficult so i hope to find the answer in this forum

You're welcome.
Do you know the definition of a vector space?

Maybe you're looking for something like : http://www.mathhelpforum.com/math-he...tor-space.html, http://www.mathhelpforum.com/math-he...ace-proof.html and http://www.mathhelpforum.com/math-he...bspaces-v.html.
Of course there are much more related threads if you start to search.