An omega automaton accepts an infinite word, if (1) there is an infinite run through the automaton, and (2) that run satisfies the acceptance condition. If the acceptance condition is simply true, then it is enough that the word has an infinite run through the automaton. That kind of omega-automaton essentially belongs to every class of nondeterministic automata, and we may consider it also as a safety automaton so that the subset construction can be used for its determinization.