0
votes
0answers
19 views

Are (certain) metric-preserving vector bundle maps proper?

Given two real vector bundles $p\colon U \to X$ and $q\colon V \to Y$ with a metric and a vector bundle map $f\colon U \to V$ preserving this metric (i.e. it's fiberwise an orthogonal map). Can we ...
6
votes
0answers
157 views

Orbit space of a free, proper G-action principal bundle

Let $G$ be a topological group and let $r \colon E \times G \to E$ be a continuous right-action on a topological space $X$. If $p\colon E \to B$ is a continuous map into a topological space $B$ such ...
1
vote
1answer
57 views

Doubt on how to prove proposition about bundles

I've started studying bundles and fiber bundles and to get some practice I've tried to prove the following proposition: "Every vector bundle $(E,B,\pi,F,G)$ is associated to a given principal bundle ...