(related to Theorem: Reduction of $\epsilon$-NFA to NFA)
For every epsilon non-deterministic finite automaton $\epsilon$-NFA there is a deterministic finite automaton. DFA accepting the same language. In other words, the class $\mathcal L(\epsilon-\operatorname{NFA})$ of all languages accepted by any $\epsilon$-NFA equals the class $\mathcal L(\operatorname{DFA})$ of all languages accepted by any DFA, formally
$$\mathcal L(\epsilon-\operatorname{NFA})=\mathcal L(\operatorname{DFA}).$$
Proofs: 1