How to prove that $r_t$ is a deformation retract
$M^a=\lbrace q\in M ; f(q)\leq a\rbrace$
We have the definition :
$r_t$ is a difformation retract if:
$r_t$ is a continius ,onto application and $r_t(q)=q , \text{for }q\in M^a$ ,
there exist an continuous application $H: M^b\times [0,1]\rightarrow M^b$ such that $H(q,0)=i_{M^a}\circ r(q); H(q,1)=I_{M^b}(q)$
M is a manifold .
$q$ and $\varphi$ are continuous so $r_t$ is continuous , but how to see that $r_t$ is onto ?
I proved that $r_0$ is the identity and $r_1$ is a retraction from $M^b$ to $M^a$ how to deduce that $r_t$ is a deformation retract ?
Please
Thank you