2. Vector spaces of functions We consider vector spaces over the field R to simplify the presentation, most results carry on to
![functional analysis - Proof that a linear map T is bounded if and only if the inverse image of the unit ball has nonempty interior - Mathematics Stack Exchange functional analysis - Proof that a linear map T is bounded if and only if the inverse image of the unit ball has nonempty interior - Mathematics Stack Exchange](https://i.stack.imgur.com/wGB7E.png)
functional analysis - Proof that a linear map T is bounded if and only if the inverse image of the unit ball has nonempty interior - Mathematics Stack Exchange
Lecture 30: Recall: Lemma: Let W be a (norm-) closed subspace of an NVS X. Let y ∈ X \ W. Then there is an f ∈ X s.t. f(y) &
![functional analysis - 1st Isomorphism Theorem For Banach Spaces: Understanding this proof. - Mathematics Stack Exchange functional analysis - 1st Isomorphism Theorem For Banach Spaces: Understanding this proof. - Mathematics Stack Exchange](https://i.stack.imgur.com/U4U0v.png)
functional analysis - 1st Isomorphism Theorem For Banach Spaces: Understanding this proof. - Mathematics Stack Exchange
![reference request - Is $(\ell^1(\mathbb N_0),\sigma(\ell^1,\ell^\infty))$ not quasi-complete? - MathOverflow reference request - Is $(\ell^1(\mathbb N_0),\sigma(\ell^1,\ell^\infty))$ not quasi-complete? - MathOverflow](https://i.stack.imgur.com/opjJK.png)