Normed Spaces

[Aysem_Kaya]

Every normed spaces is a vector space but not reverse. Necessity please proof, reverse please give a example with explanation.

 

[HallsofIvy]

Every normed spaces is a vector space but not reverse. Necessity please proof, reverse please give a example with explanation.

It looks to me like comparing the definitions of "normed space" and "vector space" will make that clear.

 

[Aysem_Kaya]

It means topological vector space

 

[HallsofIvy]

If you meant "the definition of normed space", no it doesn't. There are many different kinds of "topological vector spaces" of which "normed space" is one kind.

It appears that you do not know the precise definitions of "normed space" and "vector space". Look them up!