I would like to know the definition of Maximal interval $(T_{min}, T_{max})$ of definition for the solution of an ODE.
My professor defines the $T_{max}$ as follows:
$T_{max} $ = sup{t > t_0 such that the local solution of the CP-ODE admits a right continuation}.
But he does not define the $T_{min} $.
Is the following correct?
$T_{max} $ = inf{t < t_0 such that the local solution of the CP-ODE admits a left continuation}..