Confusion about definition of languages accepted by Turing Machine, very basic question
Even in a deterministic Turing machine, the transition function $\delta$ may be a partial function i.e. there can be pairs of states and tape symbols for which the transition function is not defined. If the Turing machine is in state $z$ and reads symbol $\alpha$ and $\delta(z,\alpha)$ is not defined then it halts. Usually the accepting states $E$ are implemented by creating states for which the transition function is undefined for all inputs i.e. the Turing machine will always halt once it enters a state $z \in E$, regardless of the symbol it reads from the tape. You may also have other halting states, but if the machine halts in a state $z \notin E$ then it has rejected the input string.