All Questions

I think the following is true and I need a reference for the proof. (Given a closed surface $S$, i.e. a compact 2-dimensional topological manifold (without boundary), we endow $S$ with a distance ...

Problem. Let $G$ be a connected Lie group and $H$ is a closed subgroup of $G$ such that the homogeneous space $G/H$ is contractible. Is $G/H$ homeomorphic to a Euclidean space $\mathbb R^n$ for some $...

Let $u$ be a smooth function on the sphere, and for each $y \in \mathbb{S}^2$, let $R_y$ be the $180^\circ$ rotation about the vector $y$. For each pair $(x, y) \in \mathbb{S}^2 \times \mathbb{S}^2$, ...

When is the group of homeomorphisms of a compact space locally compact? I am interested in finding out when the group of homeomorphisms of a compact topological space $X$ (with appropriate topology ...

Suppose $X$ is a Hausdorff (I'm happy to also assume "non compact") topological space that can be written as the topological direct limit $$\varinjlim_{a\in J} K_a$$ for $J$ a directed set ...