I am reading Brian Hall's book 'Lie groups, Lie algberas, and Representations' and on p52, corollary 2.34 reads : " Every continuous homomorphism between two matrix Lie groups is smooth."
I am wondering if this is true for general Lie groups. If not, please provide a counterexample.
What are all the properties that hold good for matrix Lie groups (and their representations) but not for general Lie groups ? It would be very helpful for me to have a list.