dg.differential geometry – Properness of moment map


Suppose a bull $ T $ Acts on a non-compact collector. $ M $. Suppose that this action is Hamiltonian and that the set of fixed points of $ T $ it's compact Let $ mu: M to mathfrak {t} ^ {*} $ denotes the map of the moment of the action, where $ mathfrak {t} $ denotes the lie algebra of $ T $.

If there is a $ X in mathfrak {t} $ such that $ mu (X): M to mathbb {R} $ is a suitable function that is limited then, why is it $ mu: M to mathfrak {t} ^ {*} $ necessarily appropriate?