All Questions

Let $k$ be a field and $V$ a $k$-vector space. Then there is a map $V \to V^{\ast \ast}$, where $V^{\ast}$ is the dual vector space. If we are in ZFC and $\dim V$ is infinite, then this map is not ...

While teaching an applied functional analysis class, I’ve noticed that students often struggle to develop an intuitive understanding of Zorn’s lemma. It’s relatively straightforward to explain why ...

Let $\Omega\subset\mathbb{R}^n$ be a bounded open set, let $$ C^1_0(\overline\Omega) = \{u\in C^1(\Omega)\cap C(\overline\Omega):u|_{\partial\Omega}=0\}, $$ and let $C^1_c(\Omega)$ be the space of ...

Many classic theorems in functional analysis involve using Baire's theorem to prove facts about topology that relate to maps between Banach spaces (or, more generally, F-spaces). The application ...

Is $E=Vect\{1,x,x^2,...,x^{2^n},...\}$ dense in $C([0,1])$ for the uniform norm? While looking for a short proof for Weierstrass' theorem, I came across this justification(*) (which shows this result)...

Usually I teach Algebra,Algebra and Geometyry, Topology, at various University levels. This semester (Spring 2014) I have to teach Differential Equations to University second year students (4th ...