suppose finite $G$ acts freely on manifold $M$ ,where "freely" means that:$\forall m\in M,g_1\cdot m=g_2 \cdot m \Leftrightarrow g_1=g_2$,
Define a relationship in $M$: if $m_1 \sim m_2$,which means that there exists $g \in G$ such that $m_1=g \cdot m_2$,then we can get a quotient space $M/G$
My problem is how to prove quotient maping :$p:M \rightarrow M/G$ has path lifting property and homotopy path lifting property