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.

2. 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.

3. 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

4. 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.

5. 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.