All Questions

Consider the space $J$ of Jordan domains on the sphere $\textbf{S}^2$, i.e., continuous injective maps from the unit disk into $\textbf{S}^2$ modulo homeomorphisms of the disk. How can one construct a ...

Let $X$ be a topological manifold of dimension $d$, and let $F$ be a collection of continuous maps from $X$ into $\mathbf{R}^d$ such that: $F$ separates points of $X$, i.e. for any two distinct ...

The question speaks for itself, but here is more details: Vector bundles are easy to motivate for students; they come up because one is trying to do "linear algebra on spaces". How does one motivate ...

I have the following question which is in some way related to an application of Randell Isotopy Theorem to complex hyperplane arrangements. Let $h,k\geq1$ be integer numbers and let $F_{1},\ldots,F_{...

I'm working on some problem in algebraic geometry. I need a reference to the following result: Let $h\in\mathbb{N}$ with $h\geq1$ and let $F\in\mathbb{C}\left[x_{1},\ldots,x_{h}\right]$ be a non ...

First let me make a definition. Let $M$ be a smooth manifold and $S \subset M $ a topological subspace of $M$. We say that $S$ has "dimenion" at most $k$ if $S$ is a subset of $$ X_1 \cup X_2 \ldots ...