The content would be

The major concept or definition of Norm is

Another major important concept is to define a sequence that converges in vector space:

While the exact mathematical definition is as follows:

As a result, there is a third important concept – subset to be subspace, requires that the subset itself is a vector space. any w can be a subset to a space, but only when w satisfy above three criteria of being a vector space can it be called subspace. Here is the lemma, a stepping stone to prove the three criteria of being vector space are met:

A trigonometric polynomial functions form a vector space.