Lie Groups and Subsemigroups with Surjective Exponential Function - Karl Heinrich Hofmann, Wolfgang Ruppert - Google Books

http://books.google.de/books?id=sZCjllhrlnsC&pg=PA158&dq=hyperspace+definition&lr=&as_brr=3#PPA25,M1

In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for…