The subspace gives information
Posted: Thu May 18, 2017 8:52 pm
Let \(\displaystyle{\left(X,||\cdot||\right)}\) be a normed space (real or complex) and \(\displaystyle{Y}\)
a linear subspace of \(\displaystyle{X}\) such that \(\displaystyle{\rm{int}(Y)\neq \varnothing}\).
Then, \(\displaystyle{X=Y}\).
a linear subspace of \(\displaystyle{X}\) such that \(\displaystyle{\rm{int}(Y)\neq \varnothing}\).
Then, \(\displaystyle{X=Y}\).