All Questions

Is there a similar statement to the constant rank theorem for finite dimensional real smooth manifolds which holds for a smooth map $F:B \rightarrow M$ where $B$ is an infinite (countable) dimensional ...

More precisely, let $M$ be a smooth manifold, $E_1$, $E_2$ vector bundles over $M$, and consider a $C^\infty(M)$-linear map $A:\Gamma(E_1) \to \Gamma(E_2)$ of vector bundles. Now consider the ...

If $V$ is an infinite dimensional vector space, for example the space of smooth functions on $\mathbb{R}$, we can introduce some differential geometry concepts by choosing a topology on $V$ and doing ...

Let $V$ be the space of $4$ by $4$ Hermitian matrices, that is a vector space of dimension $16$ over $\mathbb{R}$. Is the uniform measure of $$ \left\{ W\in Gr\left(5,V\right):W \text{contains no ...