All Questions

Let $V$ be a (Hausdorff) topological vector space, $W\subset V$ a closed linear subspace, $X\subset V $ a compact. (Q): When there is a continuous map $P:X\to W$ such that $P(x)=x$ for every $x\in X\...

It is a well known result in functional analysis that a Banach space $X$ is reflexive if and only if the unit ball is weakly compact (compact in the weak topology). This result is also known as ...

I'm interested in approximations over the so-called weighted function spaces. Let $(X,\tau_X)$ be some completely regular Hausdorff topological space. Additionally, consider some map $\psi: X \to (0,\...

It is well-known that the space of compact operators over Banach spaces is closed within the norm topology. My question: Let $X$ be a Banach space. Considering the strong topology (defined by ...

The following Theorem was described in a text I was reading as a compactness result. The proof is probably too advanced for me but I was just wondering with respect to what topology we have ...

Let $X$ be a uniform topological space and $C([0,1],X)$ the space of continuous functions from [0,1] to $X$. Assume that for subsets of $X$ sequential compactness and compactness are equivalent. Let $(...