# Lie group map whose differential is an isomorphism is a covering map

While trying to read the proof in Fulton and Harris of their “Second Principle,” I ran across something that I do not understand. They seem to claim that if $$f: G\rightarrow H$$ is a map of Lie groups whose differential $$(df)_e: \mathfrak{g}\rightarrow\mathfrak{h}$$ is an isomorphism, then f is a covering map. Can anyone provide a proof or a reference?

• Can you please make "They seem to claim that" more clearer.. I do not have the book so can not check.. can you mention clearly where it is being said? What have you tried? How do you prove some map is a covering map? – Praphulla Koushik Jan 18 at 17:55