# 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?